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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Textbook Question
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Chapter 9.5, Problem 104SE

For the following exercises, find a solution to the word problem algebraically. Then use a calculator to verify the result. Round the answer to the nearest tenth of a degree.

104. A person does a handstand with his feet touching a wall and his hands 1.5 feet away from the wall. If the person is 6 feet tall, what angle do his feet make with the wall?

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Chapter 9 Solutions

Algebra and Trigonometry

Ch. 9.1 - Verity the identity csccostan=1 .Ch. 9.1 - Show that cotcsc=cos .Ch. 9.1 - Verify the identity sin21tansintan=sin+1tan .Ch. 9.1 - Rewrite the trigonometric expression using the...Ch. 9.1 - Use algebraic techniques to verify the identity:...Ch. 9.1 - We know g(x)=cos(x) is an even function, and...Ch. 9.1 - Examine the graph of f(x)=secx on the interval [,]...Ch. 9.1 - After examining the reciprocal identity for sec t,...Ch. 9.1 - All of the Pythagorean identities are related....Ch. 9.1 - For the following exercises, use the fundamental...
Ch. 9.1 - For the following exercises, use the fundamental...Ch. 9.1 - For the following exercises, use the fundamental...Ch. 9.1 - For the following exercises, use the fundamental...Ch. 9.1 - For the following exercises, use the fundamental...Ch. 9.1 - For the following exercises, use the fundamental...Ch. 9.1 - For the following exercises, use the fundamental...Ch. 9.1 - For the following exercises, use the fundamental...Ch. 9.1 - For the following exercises, use the fundamental...Ch. 9.1 - For the following exercises, use the fundamental...Ch. 9.1 - For the following exercises, use the fundamental...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, simplify the first...Ch. 9.1 - For the following exercises, verify the identity....Ch. 9.1 - For the following exercises, verify the identity....Ch. 9.1 - For the following exercises, verify the identity....Ch. 9.1 - For the following exercises, verify the identity....Ch. 9.1 - For the following exercises, verify the identity...Ch. 9.1 - For the following exercises, prove or disprove the...Ch. 9.1 - For the following exercises, prove or disprove the...Ch. 9.1 - For the following exercises, prove or disprove the...Ch. 9.1 - For the following exercises, prove or disprove the...Ch. 9.1 - For the following exercises, prove or disprove the...Ch. 9.1 - For the following exercises, prove or disprove the...Ch. 9.1 - For the following exercises, determine whether the...Ch. 9.1 - For the following exercises, determine whether the...Ch. 9.1 - For the following exercises, determine whether the...Ch. 9.2 - Find the exact value of cos(34) .Ch. 9.2 - Find the exact value of cos(105) .Ch. 9.2 - Find the exact value of tan(23+4) .Ch. 9.2 - Write sin7 in terms of its cofunction.Ch. 9.2 - Verify the identity: tan()=tan .Ch. 9.2 - Explain the basis for the cofunction identities...Ch. 9.2 - Is there only one way to evaluate cos(54) ?...Ch. 9.2 - Explain to someone who has forgotten the even-odd...Ch. 9.2 - For the following exercises, find the exact value...Ch. 9.2 - For the following exercises, find the exact value....Ch. 9.2 - For the following exercises, find the exact value....Ch. 9.2 - For the following exercises, find the exact value....Ch. 9.2 - For the following exercises, find the exact value....Ch. 9.2 - For the following exercises, find the exact value....Ch. 9.2 - For the following exercises, rewrite in terms of...Ch. 9.2 - For the following exercises, rewrite in terms of...Ch. 9.2 - For the following exercises, rewrite in terms of...Ch. 9.2 - For the following exercises, rewrite in terms of...Ch. 9.2 - For the following exercises, simplify the given...Ch. 9.2 - For the following exercises, simplify the given...Ch. 9.2 - For the following exercises, simplify the given...Ch. 9.2 - For the following exercises, simplify the given...Ch. 9.2 - For the following exercises, simplify the given...Ch. 9.2 - For the following exercises, simplify the given...Ch. 9.2 - For the following exercises, find the requested...Ch. 9.2 - For the following exercises, find the requested...Ch. 9.2 - For the following exercises, find the exact value...Ch. 9.2 - For the following exercises, find the exact value...Ch. 9.2 - For the following exercises, find the exact value...Ch. 9.2 - For the following exercises, simplify the...Ch. 9.2 - For the following exercises, simplify the...Ch. 9.2 - For the following exercises, simplify the...Ch. 9.2 - For the following exercises, simplify the...Ch. 9.2 - For the following exercises, simplify the...Ch. 9.2 - For the following exercises, simplify the...Ch. 9.2 - For the following exercises, simplify the...Ch. 9.2 - For the following exercises, simplify the...Ch. 9.2 - For the following exercises, use a graph to...Ch. 9.2 - For the following exercises, use a graph to...Ch. 9.2 - For the following exercises, use a graph to...Ch. 9.2 - For the following exercises, use a graph to...Ch. 9.2 - For the following exercises, use a graph to...Ch. 9.2 - For the following exercises, use a graph to...Ch. 9.2 - For the following exercises, use a graph to...Ch. 9.2 - For the following exercises, use a graph to...Ch. 9.2 - For the following exercises, use a graph to...Ch. 9.2 - For the following exercises, find the exact value...Ch. 9.2 - For the following exercises, find the exact value...Ch. 9.2 - For the following exercises, find the exact value...Ch. 9.2 - For the following exercises, find the exact value...Ch. 9.2 - For the following exercises, find the exact value...Ch. 9.2 - For the following exercises, prove the identities...Ch. 9.2 - For the following exercises, prove the identities...Ch. 9.2 - For the following exercises, prove the identities...Ch. 9.2 - For the following exercises, prove the identities...Ch. 9.2 - For the following exercises, prove the identities...Ch. 9.2 - For the following exercises, prove or disprove the...Ch. 9.2 - For the following exercises, prove or disprove the...Ch. 9.2 - For the following exercises, prove or disprove the...Ch. 9.2 - For the following exercises, prove or disprove the...Ch. 9.2 - For the following exercises, prove or disprove the...Ch. 9.3 - Given sin=58 , with in quadrant I, find (2) .Ch. 9.3 - Verify the identity: cos4sin4=cos(2) .Ch. 9.3 - Verify the identity: cos(2)cos=cos3cossin2.Ch. 9.3 - Use the power-reducing formulas to prove that...Ch. 9.3 - Given that sin=45 and lies in quadrant IV, find...Ch. 9.3 - Explain how to determine the reduction identities...Ch. 9.3 - Explain how to determine the double-angle formula...Ch. 9.3 - We can determine the half-angle formula for...Ch. 9.3 - For the half-angle formula given in the previous...Ch. 9.3 - For the following exercises, find the exact values...Ch. 9.3 - For the following exercises, find the exact values...Ch. 9.3 - For the following exercises, find the exact values...Ch. 9.3 - For the following exercises, find the exact values...Ch. 9.3 - For the following exercises, find the values of...Ch. 9.3 - For the following exercises, find the values of...Ch. 9.3 - For the following exercises, simplify to one...Ch. 9.3 - For the following exercises, simplify to one...Ch. 9.3 - For the following exercises, find the exact value...Ch. 9.3 - For the following exercises, find the exact value...Ch. 9.3 - For the following exercises, find the exact value...Ch. 9.3 - For the following exercises, find the exact value...Ch. 9.3 - For the following exercises, find the exact value...Ch. 9.3 - For the following exercises, find the exact value...Ch. 9.3 - For the following exercises, find the exact value...Ch. 9.3 - For the following exercises, find the exact values...Ch. 9.3 - For the following exercises, find the exact values...Ch. 9.3 - For the following exercises, find the exact values...Ch. 9.3 - For the following exercises, find the exact values...Ch. 9.3 - For the following exercises, use Figure 5 to find...Ch. 9.3 - For the following exercises, use Figure 5 to find...Ch. 9.3 - For the following exercises, use Figure 5 to find...Ch. 9.3 - For the following exercises, use Figure 5 to find...Ch. 9.3 - For the following exercises, simplify each...Ch. 9.3 - For the following exercises, simplify each...Ch. 9.3 - For the following exercises, simplify each...Ch. 9.3 - For the following exercises, simplify each...Ch. 9.3 - For the following exercises, simplify each...Ch. 9.3 - For the following exercises, simplify each...Ch. 9.3 - For the following exercises, prove the identity...Ch. 9.3 - For the following exercises, prove the identity...Ch. 9.3 - For the following exercises, prove the identity...Ch. 9.3 - For the following exercises, prove the identity...Ch. 9.3 - For the following exercises, rewrite the...Ch. 9.3 - For the following exercises, rewrite the...Ch. 9.3 - For the following exercises, rewrite the...Ch. 9.3 - For the following exercises, rewrite the...Ch. 9.3 - For the following exercises, rewrite the...Ch. 9.3 - For the following exercises, rewrite the...Ch. 9.3 - For the following exercises, rewrite the...Ch. 9.3 - For the following exercises, reduce the equations...Ch. 9.3 - For the following exercises, reduce the equations...Ch. 9.3 - For the following exercises, reduce the equations...Ch. 9.3 - For the following exercises, reduce the equations...Ch. 9.3 - For the following exercises, reduce the equations...Ch. 9.3 - For the following exercises, reduce the equations...Ch. 9.3 - For the following exercises, reduce the equations...Ch. 9.3 - For the following exercises, reduce the equations...Ch. 9.3 - For the following exercises, algebraically find an...Ch. 9.3 - For the following exercises, algebraically find an...Ch. 9.3 - For the following exercises, prove the identities....Ch. 9.3 - For the following exercises, prove the identities....Ch. 9.3 - For the following exercises, prove the identities....Ch. 9.3 - For the following exercises, prove the identities....Ch. 9.3 - For the following exercises, prove the identities....Ch. 9.3 - For the following exercises, prove the identities....Ch. 9.3 - For the following exercises, prove the identities....Ch. 9.3 - For the following exercises, prove the identities....Ch. 9.3 - For the following exercises, prove the identities...Ch. 9.4 - Use the product-to-sum formula to write the...Ch. 9.4 - Use the product-to-sum formula to write the...Ch. 9.4 - Use the product to-sum formula to evaluate...Ch. 9.4 - Use the sum-to-product formula to write the sum as...Ch. 9.4 - Verify the identity tancotcos2=sin2 .Ch. 9.4 - Starting with the product to sum formula...Ch. 9.4 - Provide two different methods of calculating...Ch. 9.4 - Describe a situation where we would convert an...Ch. 9.4 - Describe a situation where we would convert an...Ch. 9.4 - For the following exercises, rewrite the product...Ch. 9.4 - For the following exercises, rewrite the product...Ch. 9.4 - For the following exercises, rewrite the product...Ch. 9.4 - For the following exercises, rewrite the product...Ch. 9.4 - For the following exercises, rewrite the product...Ch. 9.4 - For the following exercises, rewrite the product...Ch. 9.4 - For the following exercises, rewrite the sum or...Ch. 9.4 - For the following exercises, rewrite the sum or...Ch. 9.4 - For the following exercises, rewrite the sum or...Ch. 9.4 - For the following exercises, rewrite the sum or...Ch. 9.4 - For the following exercises, rewrite the sum or...Ch. 9.4 - For the following exercises, rewrite the sum or...Ch. 9.4 - For the following exercises, evaluate the product...Ch. 9.4 - For the following exercises, evaluate the product...Ch. 9.4 - For the following exercises, evaluate the product...Ch. 9.4 - For the following exercises, evaluate the product...Ch. 9.4 - For the following exercises, evaluate the product...Ch. 9.4 - For the following exercises, evaluate the product...Ch. 9.4 - For the following exercises, evaluate the product...Ch. 9.4 - For the following exercises, evaluate the product...Ch. 9.4 - For the following exercises, evaluate the product...Ch. 9.4 - For the following exercises, evaluate the product...Ch. 9.4 - For the following exercises, rewrite the sum as a...Ch. 9.4 - For the following exercises, rewrite the sum as a...Ch. 9.4 - For the following exercises, rewrite the sum as a...Ch. 9.4 - For the following exercises, rewrite the sum as a...Ch. 9.4 - For the following exercises, rewrite the sum as a...Ch. 9.4 - For the following exercises, prove the identity....Ch. 9.4 - For the following exercises, prove the identity....Ch. 9.4 - For the following exercises, prove the identity....Ch. 9.4 - For the following exercises, prove the identity....Ch. 9.4 - For the following exercises, prove the identity....Ch. 9.4 - 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[Hint: Make a substitution...Ch. 9.5 - Solve the quadratic equation 2cos2+cos=0 .Ch. 9.5 - Will there always be solutions to trigonometric...Ch. 9.5 - When solving a trigonometric equation involving...Ch. 9.5 - When solving linear trig equations in terms of...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, solve exactly on...Ch. 9.5 - For the following exercises, solve exactly on...Ch. 9.5 - For the following exercises, solve exactly on...Ch. 9.5 - For the following exercises, solve exactly on...Ch. 9.5 - 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For the following exercises, solve with the...Ch. 9.5 - For the following exercises, solve with the...Ch. 9.5 - For the following exercises, solve with the...Ch. 9.5 - For the following exercises, solve with the...Ch. 9.5 - For the following exercises, solve with the...Ch. 9.5 - For the following exercises, solve with the...Ch. 9.5 - For the following exercises, solve exactly on the...Ch. 9.5 - For the following exercises, solve exactly on the...Ch. 9.5 - For the following exercises, solve exactly on the...Ch. 9.5 - For the following exercises, solve exactly on the...Ch. 9.5 - For the following exercises, solve exactly on the...Ch. 9.5 - For the following exercises, solve exactly on the...Ch. 9.5 - For the following exercises, solve exactly on the...Ch. 9.5 - For the following exercises, solve exactly on the...Ch. 9.5 - For the following exercises, solve exactly on the...Ch. 9.5 - For the following exercises, find exact solutions...Ch. 9.5 - For the following exercises, find exact solutions...Ch. 9.5 - 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For the following exercises, algebraically...Ch. 9.5 - For the following exercises, algebraically...Ch. 9.5 - For the following exercises, algebraically...Ch. 9.5 - For the following exercises, algebraically...Ch. 9.5 - For the following exercises, use a calculator to...Ch. 9.5 - For the following exercises, use a calculator to...Ch. 9.5 - For the following exercises, use a calculator to...Ch. 9.5 - For the following exercises, use a calculator to...Ch. 9.5 - For the following exercises, solve the equations...Ch. 9.5 - For the following exercises, solve the equations...Ch. 9.5 - For the following exercises, solve the equations...Ch. 9.5 - For the following exercises, solve the equations...Ch. 9.5 - For the following exercises, solve the equations...Ch. 9.5 - For the following exercises, solve the equations...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - For the following exercises, find all solutions...Ch. 9.5 - An airplane has only enough gas to fly to a city...Ch. 9.5 - If a loading ramp is placed next to a truck, at a...Ch. 9.5 - If a loading ramp is placed next to a truck, at a...Ch. 9.5 - A woman is watching a launched rocket currently 11...Ch. 9.5 - An astronaut is in a launched rocket currently 15...Ch. 9.5 - A woman is standing 8 meters away from a 10-meter...Ch. 9.5 - A man is standing 10 meters away from a 6-meter...Ch. 9.5 - A 20-foot tall building has a shadow that is 55...Ch. 9.5 - A 90-foot tall building has a shadow that is 2...Ch. 9.5 - A spotlight on the ground 3 meters from a 2-meter...Ch. 9.5 - A spotlight on the ground 3 feet from a 5-foot...Ch. 9.5 - For the following exercises, find a solution to...Ch. 9.5 - For the following exercises, find a solution to...Ch. 9.5 - For the following exercises, find a solution to...Ch. 9 - For the following exercises, find all solutions...Ch. 9 - For the following exercises, find all solutions...Ch. 9 - For the following exercises, find all solutions...Ch. 9 - For the following exercises, find all solutions...Ch. 9 - For the following exercises, find all solutions...Ch. 9 - For the following exercises, find all solutions...Ch. 9 - For the following exercises, use basic identities...Ch. 9 - For the following exercises, use basic identities...Ch. 9 - For the following exercises, determine if the...Ch. 9 - For the following exercises, determine if the...Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the Following exercises, find the exact value...Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, prove the identity....Ch. 9 - For the following exercises, prove the identity....Ch. 9 - For the following exercises, simplify the...Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, use Figure 1 to find...Ch. 9 - For the following exercises, use Figure 1 to find...Ch. 9 - For the following exercises, prove the identity....Ch. 9 - For the following exercises, prove the identity....Ch. 9 - For the following exercises, rewrite the...Ch. 9 - For the following exercises, rewrite the...Ch. 9 - For the following exercises, evaluate the product...Ch. 9 - For the following exercises, evaluate the product...Ch. 9 - For the following exercises, evaluate the product...Ch. 9 - For the following exercises, evaluate the sum by...Ch. 9 - For the following exercises, evaluate the sum by...Ch. 9 - For the following exercises, change the functions...Ch. 9 - For the following exercises, change the functions...Ch. 9 - For the following exercises, change the functions...Ch. 9 - For the following exercises, change the functions...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, simplify the equation...Ch. 9 - For the following exercises, simplify the equation...Ch. 9 - For the following exercises, graph each side of...Ch. 9 - For the following exercises, graph each side of...Ch. 9 - For the following exercises, simplify the given...Ch. 9 - For the following exercises, simplify the given...Ch. 9 - For the following exercises, simplify the given...Ch. 9 - For the following exercises, simplify the given...Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, find the exact value....Ch. 9 - For the following exercises, simplify each...Ch. 9 - For the following exercises, simplify each...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, find all exact...Ch. 9 - Rewrite the sum as a product: cos(2x)+cos(8x) .Ch. 9 - Rewrite the product as a sum or difference:...Ch. 9 - Rewrite the difference as a product: 2sin(8)sin(4)Ch. 9 - Find all solutions of tan(x)3=0 .Ch. 9 - Find the solutions of sec2x2secx=15 on the...Ch. 9 - For the following exercises, find all exact...Ch. 9 - For the following exercises, find all exact...Ch. 9 - Find sin(2),cos(2),andtan(2) given cot=34 and is...Ch. 9 - Find sin(2),cos(2),andtan(2) given cot=725 and is...Ch. 9 - Rewrite the expression sin4x with no powers...Ch. 9 - For the following exercises, prove the identity....Ch. 9 - For the following exercises, prove the identity....Ch. 9 - For the following exercises, prove the identity....Ch. 9 - Plot the points and find a function of the form...Ch. 9 - The displacement h(t) in centimeters of a mass...Ch. 9 - A woman is standing 300 feet away from a 2,000-...Ch. 9 - Two frequencies of sound are played on an...Ch. 9 - The average monthly snowfall in a small village in...Ch. 9 - A spring attached to a ceiling is pulled down 20...Ch. 9 - Water levels near a glacier currently average 9...
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