PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Trigonometric Identities
Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.
Inverse Trigonometric Functions
Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosi…
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Question
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Chapter 5.4, Problem 21E
To determine

To find: the exact values of the sine, cosine and tangent of the angle.

Expert Solution & Answer
Check Mark

Answer to Problem 21E

  sin(−105°)=−6+24,cos(−105°)=−6+24,tan(−105°)=2+3 .

Explanation of Solution

Given information:

Given angle,

  (−105°)

Formula used:

  sin(−θ)=−sinθcos(−θ)=cosθtan(−θ)=−tanθ

And

  sin(u+v)=sinucosv+cosusinvcos(u+v)=cosucosv−sinusinvtan(u+v)=tanu+tanv1−tanutanv

Calculation:

Find the value of sine, cosine and tangent of the angle (−105°) by using the sum formulas as follows

  sin(−105°)=−sin105°=−sin(60°+45°)=−(sin60°cos45°+cos60°sin45°)=−(32)(12)−(12)(12)=−322−(122)=−3+122=−6+24

Now for cosine we get

  cos(−105°)=cos105°=cos(60°+45°)=cos60°cos45°−sin60°sin45°=(12)(12)−(32)(12)=122−(322)=1−322=2−64

Also for tangent we get

  tan(−105°)=−tan105°=−tan(60°+45°)=−tan60°+tan45°1−tan60°tan45°=−3+11−3(1)=−3+11−3

After rationalizing,

  tan(−105°)=−3+11−3(3+13+1)=−3+1+231−3=2+3

Hence, sin(−105°)=−6+24,cos(−105°)=−6+24,tan(−105°)=2+3 .

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Chapter 5.4, Problem 20E
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Chapter 5.4, Problem 22E

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - Prob. 67ECh. 5.4 - Prob. 68ECh. 5.4 - Prob. 69ECh. 5.4 - Prob. 70ECh. 5.4 - Prob. 71ECh. 5.4 - Prob. 72ECh. 5.4 - Prob. 73ECh. 5.4 - Prob. 74ECh. 5.4 - Prob. 75ECh. 5.4 - Prob. 76ECh. 5.4 - Prob. 77ECh. 5.4 - Prob. 78ECh. 5.4 - Prob. 79ECh. 5.4 - Prob. 80ECh. 5.4 - Prob. 81ECh. 5.4 - Prob. 82ECh. 5.4 - Prob. 83ECh. 5.4 - Prob. 84ECh. 5.4 - Prob. 85ECh. 5.4 - Prob. 86ECh. 5.4 - Prob. 87ECh. 5.4 - Prob. 88ECh. 5.4 - Prob. 89ECh. 5.4 - Prob. 90ECh. 5.4 - Prob. 91ECh. 5.4 - Prob. 92ECh. 5.4 - Prob. 93ECh. 5.4 - Prob. 94ECh. 5.4 - Prob. 95ECh. 5.4 - Prob. 96ECh. 5.4 - Prob. 97ECh. 5.4 - Prob. 98ECh. 5.4 - Prob. 99ECh. 5.4 - Prob. 100ECh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - 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Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
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