Algebra and Trigonometry
Algebra and Trigonometry
1st Edition
ISBN: 9781938168376
Author: Jay Abramson
Publisher: OpenStax
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Concept explainers

Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
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Chapter 7.2, Problem 25SE

For the following exercises, use Figure 15 to evaluate each trigonometric function of angled

Chapter 7.2, Problem 25SE, For the following exercises, use Figure 15 to evaluate each trigonometric function of angled 25.

25. tan   A

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Chapter 7 Solutions

Algebra and Trigonometry

Ch. 7.1 - Show an angle of 240° on a circle in standard...Ch. 7.1 - Find the radian measure of three-fourths of a full...Ch. 7.1 - Convert 34 radians to degrees.Ch. 7.1 - Convert 126° to radians.Ch. 7.1 - Find an angle that is coterminal with an angle...Ch. 7.1 - Find an angle that is coterminal with an angle...Ch. 7.1 - Find an angle of measure that is coterminal with...Ch. 7.1 - Find the arc length along a circle of radius 10...Ch. 7.1 - In central pivot irrigation, a large irrigation...Ch. 7.1 - An old vinyl record is played on a turntable...
Ch. 7.1 - A satellite is rotating around Earth at 0.25...Ch. 7.1 - Draw an angle in standard position. Label the...Ch. 7.1 - Explain why there are an infinite number of angles...Ch. 7.1 - State what a positive or negative angle signifies,...Ch. 7.1 - How does radian measure of an angle compare to the...Ch. 7.1 - Explain the differences between linear speed and...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, draw an angle in...Ch. 7.1 - For the following exercises, refer to Figure 25....Ch. 7.1 - For the following exercises, refer to Figure 25....Ch. 7.1 - For the following exercises, refer to Figure 26....Ch. 7.1 - For the following exercises, refer to Figure 26....Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, convert angles in...Ch. 7.1 - For the following exercises, use to given...Ch. 7.1 - For the following exercises, use to given...Ch. 7.1 - For the following exercises, use to given...Ch. 7.1 - For the following exercises, use to given...Ch. 7.1 - For the following exercises, use to given...Ch. 7.1 - For the following exercises, use to given...Ch. 7.1 - For the following exercises, use the given...Ch. 7.1 - For the following exercises, use the given...Ch. 7.1 - For the following exercises, use the given...Ch. 7.1 - For the following exercises, use the given...Ch. 7.1 - For the following exercises, find the angle...Ch. 7.1 - For the following exercises, find the angle...Ch. 7.1 - For the following exercises, find the angle...Ch. 7.1 - For the following exercises, find the angle...Ch. 7.1 - For the following exercises, find the angle...Ch. 7.1 - For the following exercises, find the angle...Ch. 7.1 - For the following exercises, find the angle...Ch. 7.1 - For the following exercises, find the angle...Ch. 7.1 - A truck with 32-inch diameter wheels is traveling...Ch. 7.1 - A bicycle with 24-inch diameter wheels is...Ch. 7.1 - A wheel of radius 8 inches is rotating 15°/s. What...Ch. 7.1 - A wheel of radius 14 inches is rotating 0.5 rad/s....Ch. 7.1 - A CD has diameter of 120 millimeters. When playing...Ch. 7.1 - When being burned in a writable CD-R drive, the...Ch. 7.1 - A person is standing on the equator of Earth...Ch. 7.1 - Find the distance along an arc on the surface of...Ch. 7.1 - Find the distance along an arc on the surface of...Ch. 7.1 - Consider a clock with an hour hand and minute...Ch. 7.1 - Two cities have the same longitude. The latitude...Ch. 7.1 - A city is located at 40 degrees north latitude....Ch. 7.1 - A city is located at 75 degrees north latitude....Ch. 7.1 - Find the linear speed of the moon if the average...Ch. 7.1 - A bicycle has wheels 28 inches in diameter. A...Ch. 7.1 - A car travels 3 miles. Its tires make 2640...Ch. 7.1 - A wheel on a tractor has a 24-inch diameter. How...Ch. 7.2 - Given the triangle shown in Figure 4, find the...Ch. 7.2 - Using the triangle shown in Figure 7, evaluate...Ch. 7.2 - Find the exact value of the trigonometric...Ch. 7.2 - If csc(6)=2 , find sec(3) .Ch. 7.2 - A right triangle has one angle of 3 and a...Ch. 7.2 - How long a ladder is needed to reach a windowsill...Ch. 7.2 - For the given right triangle, label the adjacent...Ch. 7.2 - When a right triangle with a hypotenuse of 1 is...Ch. 7.2 - The tangent of an angle compares which sides of...Ch. 7.2 - What is the relationship between the two acute...Ch. 7.2 - Explain the cofunction identity.Ch. 7.2 - For the following exercises, use cofunctions of...Ch. 7.2 - For the following exercises, use cofunctions of...Ch. 7.2 - For the following exercises, use cofunctions of...Ch. 7.2 - For the following exercises, use cofunctions of...Ch. 7.2 - For the following exercises, find the lengths of...Ch. 7.2 - For the following exercises, find the lengths of...Ch. 7.2 - For the following exercises, find the lengths of...Ch. 7.2 - For the following exercises, find the lengths of...Ch. 7.2 - For the following exercises, find the lengths of...Ch. 7.2 - For the following exercises, find the lengths of...Ch. 7.2 - For the following exercises, find the lengths of...Ch. 7.2 - For the following exercises, use Figure 14 to...Ch. 7.2 - For the following exercises, use Figure 14 to...Ch. 7.2 - For the following exercises, use Figure 14 to...Ch. 7.2 - For the following exercises, use Figure 14 to...Ch. 7.2 - For the following exercises, use Figure 14 to...Ch. 7.2 - For the following exercises, use Figure 14 to...Ch. 7.2 - For the following exercises, use Figure 15 to...Ch. 7.2 - For the following exercises, use Figure 15 to...Ch. 7.2 - For the following exercises, use Figure 15 to...Ch. 7.2 - For the following exercises, use Figure 15 to...Ch. 7.2 - For the following exercises, use Figure 15 to...Ch. 7.2 - For the following exercises, use Figure 15 to...Ch. 7.2 - For the following exercises, solve for the unknown...Ch. 7.2 - For the following exercises, solve for the unknown...Ch. 7.2 - For the following exercises, solve for the unknown...Ch. 7.2 - For the following exercises, use a calculator to...Ch. 7.2 - For the following exercises, use a calculator to...Ch. 7.2 - For the following exercises, use a calculator to...Ch. 7.2 - For the following exercises, use a calculator to...Ch. 7.2 - For the following exercises, use a calculator to...Ch. 7.2 - For the following exercises, use a calculator to...Ch. 7.2 - For the following exercises, use a calculator to...Ch. 7.2 - For the following exercises, use a calculator to...Ch. 7.2 - For the following exercises, use a calculator to...Ch. 7.2 - For the following exercises, use a calculator to...Ch. 7.2 - Find x.Ch. 7.2 - Find x.Ch. 7.2 - Find x.Ch. 7.2 - Find x.Ch. 7.2 - A radio tower is located 400 feet from a building....Ch. 7.2 - A radio tower is located 325 feet from a building....Ch. 7.2 - A 200-foot tall monument is located in the...Ch. 7.2 - A 400-foot tall monument is located in the...Ch. 7.2 - There is an antenna on the top of a building. From...Ch. 7.2 - There is lightning rod on the top of a building....Ch. 7.2 - A 33-ft ladder leans against a building so that...Ch. 7.2 - A 23-ft ladder leans against a building so that...Ch. 7.2 - The angle of elevation to the top of a building in...Ch. 7.2 - The angle of elevation to the top of a building in...Ch. 7.2 - Assuming that a 370-foot tall giant redwood grows...Ch. 7.3 - A certain angle t corresponds to a point on the...Ch. 7.3 - Find cosine and sine of the angle .Ch. 7.3 - If cos(t)=2425 and t is in the fourth quadrant,...Ch. 7.3 - Evaluate sin(3) .Ch. 7.3 - Find the reference angle of 53 .Ch. 7.3 - a. Use the reference angle of 315° to find...Ch. 7.3 - Find the coordinates of the point on the unit...Ch. 7.3 - Describe the unit circle.Ch. 7.3 - What do the x- and y-coordinates of the points on...Ch. 7.3 - Discuss the difference between a coterminal angle...Ch. 7.3 - Explain how the cosine of an angle in the second...Ch. 7.3 - Explain how the sine of an angle in the second...Ch. 7.3 - For the following exercises, use the given sign of...Ch. 7.3 - For the following exercises, use the given sign of...Ch. 7.3 - For the following exercises, use the given sign of...Ch. 7.3 - For the following exercises, use the given sign of...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, find the exact value...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, state the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the reference...Ch. 7.3 - For the following exercises, find the requested...Ch. 7.3 - For the following exercises, find the requested...Ch. 7.3 - For the following exercises, find the requested...Ch. 7.3 - For the following exercises, find the requested...Ch. 7.3 - For the following exercises, find the requested...Ch. 7.3 - For the following exercises, find the requested...Ch. 7.3 - For the following exercises, find the requested...Ch. 7.3 - For the following exercises, find the requested...Ch. 7.3 - For the following exercises, find the requested...Ch. 7.3 - For the following exercises, find the requested...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use the given point...Ch. 7.3 - For the following exercises, use a graphing...Ch. 7.3 - For the following exercises, use a graphing...Ch. 7.3 - For the following exercises, use a graphing...Ch. 7.3 - For the following exercises, use a graphing...Ch. 7.3 - For the following exercises, use a graphing...Ch. 7.3 - For the following exercises, use a graphing...Ch. 7.3 - For the following exercises, use a graphing...Ch. 7.3 - For the following exercises, use a graphing...Ch. 7.3 - For the following exercises, use a graphing...Ch. 7.3 - For the following exercises, use a graphing...Ch. 7.3 - For the following exercises, evaluate. 90....Ch. 7.3 - For the following exercises, evaluate. 91....Ch. 7.3 - For the following exercises, evaluate. 92....Ch. 7.3 - For the following exercises, evaluate. 93....Ch. 7.3 - For the following exercises, evaluate. 94....Ch. 7.3 - For the following exercises, evaluate. 95....Ch. 7.3 - For the following exercises, evaluate. 96....Ch. 7.3 - For the following exercises, evaluate. 97....Ch. 7.3 - For the following exercises, evaluate. 98....Ch. 7.3 - For the following exercises, evaluate. 99....Ch. 7.3 - For the following exercises, use this scenario: A...Ch. 7.3 - For the following exercises, use this scenario: A...Ch. 7.3 - For the following exercises, use this scenario: A...Ch. 7.3 - For the following exercises, use this scenario: A...Ch. 7.3 - For the following exercises, use this scenario: A...Ch. 7.4 - The point (22,22) is on the unit circle, as shown...Ch. 7.4 - Find sint,cost,tant,sect,csct,andcott when t=3 ....Ch. 7.4 - Use reference angles to find all six trigonometric...Ch. 7.4 - If the cotangent of angle t is 3 , what is the...Ch. 7.4 - Evaluate csc(76) .Ch. 7.4 - Simplify (tant)(cost) .Ch. 7.4 - If sec(t)=178 and 0t,, find the values of the...Ch. 7.4 - Find the values of the six trigonometric functions...Ch. 7.4 - If sin(t)=22 and cos(t)=22 , find...Ch. 7.4 - Evaluate the cotangent of 8 .Ch. 7.4 - On an interval of [0,2) , can the sine and cosine...Ch. 7.4 - What would you estimate the cosine of degrees to...Ch. 7.4 - For any angle in quadrant II, if you knew the sine...Ch. 7.4 - Describe the secant function.Ch. 7.4 - Tangent and cotangent have a period of . What does...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - ]For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, find the exact value...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - ]For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use reference angles...Ch. 7.4 - For the following exercises, use the angle in the...Ch. 7.4 - For the following exercises, use the angle in the...Ch. 7.4 - For the following exercises, use the angle in the...Ch. 7.4 - For the following exercises, use a graphing...Ch. 7.4 - For the following exercises, use a graphing...Ch. 7.4 - For the following exercises, use a graphing...Ch. 7.4 - For the following exercises, use a graphing...Ch. 7.4 - For the following exercises, use a graphing...Ch. 7.4 - For the following exercises, use a graphing...Ch. 7.4 - For the following exercises, use a graphing...Ch. 7.4 - For the following exercises, use a graphing...Ch. 7.4 - For the following exercises, use a graphing...Ch. 7.4 - For the following exercises, use a graphing...Ch. 7.4 - For the following exercises, use identities to...Ch. 7.4 - For the following exercises, use identities to...Ch. 7.4 - For the following exercises, use identities to...Ch. 7.4 - For the following exercises, use identities to...Ch. 7.4 - For the following exercises, use identities to...Ch. 7.4 - For the following exercises, use identities to...Ch. 7.4 - For the following exercises, use identities to...Ch. 7.4 - For the following exercises, use identities to...Ch. 7.4 - For the following exercises, use identities to...Ch. 7.4 - For the following exercises, use identities to...Ch. 7.4 - The amount of sunlight in a certain city can be...Ch. 7.4 - The amount of sunlight in a certain city can be...Ch. 7.4 - The equation P=20sin(2t)+100 models the blood...Ch. 7.4 - The height of a piston, h, in inches, can be...Ch. 7.4 - The height of a piston, h, in inches, can be...Ch. 7 - For the following exercises, convert the angle...Ch. 7 - For the following exercises, convert the angle...Ch. 7 - For the following exercises, convert the angle...Ch. 7 - For the following exercises, convert the angle...Ch. 7 - For the following exercises, convert the angle...Ch. 7 - For the following exercises, convert the angle...Ch. 7 - For the following exercises, find the angle...Ch. 7 - For the following exercises, find the angle...Ch. 7 - For the following exercises, find the angle...Ch. 7 - For the following exercises, find the angle...Ch. 7 - For the following exercises, draw the angle...Ch. 7 - For the following exercises, draw the angle...Ch. 7 - For the following exercises, draw the angle...Ch. 7 - For the following exercises, draw the angle...Ch. 7 - For the following exercises, draw the angle...Ch. 7 - For the following exercises, draw the angle...Ch. 7 - For the following exercises, use side lengths to...Ch. 7 - For the following exercises, use side lengths to...Ch. 7 - For the following exercises, use side lengths to...Ch. 7 - For the following exercises, use side lengths to...Ch. 7 - For the following exercises, use side lengths to...Ch. 7 - For the following exercises, use the given...Ch. 7 - For the following exercises, use the given...Ch. 7 - For the following exercises, use Figure 1 to...Ch. 7 - For the following exercises, use Figure 1 to...Ch. 7 - For the following exercises, solve for the unknown...Ch. 7 - For the following exercises, solve for the unknown...Ch. 7 - For the following exercises, solve for the unknown...Ch. 7 - For the following exercises, solve for the unknown...Ch. 7 - Find the exact value of sin3 .Ch. 7 - Find the exact value of cos4 .Ch. 7 - Find the exact value of cos .Ch. 7 - State the reference angle for 300 .Ch. 7 - State the reference angle for 34 .Ch. 7 - Compute cosine of 330 .Ch. 7 - Compute sine of 54 .Ch. 7 - State the domain of the sine and cosine functions.Ch. 7 - State the range of the sine and cosine functions.Ch. 7 - For the following exercises, find the exact value...Ch. 7 - For the following exercises, find the exact value...Ch. 7 - For the following exercises, find the exact value...Ch. 7 - For the following exercises, find the exact value...Ch. 7 - For the following exercises, use reference angles...Ch. 7 - For the following exercises, use reference angles...Ch. 7 - For the following exercises, use reference angles...Ch. 7 - For the following exercises, use reference angles...Ch. 7 - For the following exercises, use reference angles...Ch. 7 - For the following exercises, use reference angles...Ch. 7 - For the following exercises, use reference angles...Ch. 7 - For the following exercises, use reference angles...Ch. 7 - Convert 56 radians to degrees.Ch. 7 - Convert —620° to radians.Ch. 7 - Find the length of a circular arc with a radius 12...Ch. 7 - Find the area of the sector with radius of 8 feet...Ch. 7 - Find the angle between 0° and 360° that is...Ch. 7 - Find the angle between 0 and 2 in radians that is...Ch. 7 - Draw the angle 315° in standard position on the...Ch. 7 - Draw the angle 6 in standard position on the...Ch. 7 - A carnival has a Ferris wheel with a diameter of...Ch. 7 - Find the missing sides of the triangle ABC:...Ch. 7 - Find the missing sides of the triangle.Ch. 7 - The angle of elevation to the top of a building in...Ch. 7 - Find the exact value of sin sin6Ch. 7 - Compute sine of 240 .Ch. 7 - State the domain of the sine and cosine functions.Ch. 7 - State the range of the sine and cosine functions.Ch. 7 - Find the exact value of cot4 .Ch. 7 - Find the exact value of tan3 .Ch. 7 - Use reference angles to evaluate csc74 .Ch. 7 - Use reference angles to evaluate tan210 .Ch. 7 - If csct=0.68 , what is the csc(t) ?Ch. 7 - If cost=32 , find cos(t2) .Ch. 7 - Find the missing angle: cos(6)=sin(_)
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Trigonometric Ratios; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9-eHMMpQC2k;License: Standard YouTube License, CC-BY