Algebra and Trigonometry
Algebra and Trigonometry
1st Edition
ISBN: 9781938168376
Author: Jay Abramson
Publisher: OpenStax
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Fundamentals of Trigonometric Identities
Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.
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Chapter 7.3, Problem 94SE

For the following exercises, evaluate.

94. sin  ( π 6 ) cos ( − π 3 )

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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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