Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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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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Chapter 5, Problem 90RE
To determine

To find: the exact value of sin2u,cos2u and tan2u , using the double angle formulas.

Expert Solution & Answer
Check Mark

Answer to Problem 90RE

  sin2u=−2425cos(2u)=725tan(2u)=−247 .

Explanation of Solution

Given information:

Given trigonometric ratio

  cosu=45,     3π2<u<2π .

Calculation:

Consider the ratio

  cosu=45,     3π2<u<2π

Find sin2u using double angle formula. The cosine of an angle is equal to adjacent side over the hypotenuse. Since;

  cosu=45

Apply Pythagorean Theorem to find length of opposite side;

  =52−42=±9=±3

Take only −3 because 3π2<u<π , draw the triangle;

  Precalculus with Limits: A Graphing Approach, Chapter 5, Problem 90RE

Therefore;

  sinu=OppositeHypotenuse=−35

And,

  tanu=Oppositeadjacent=−34

Apply double angle formula sin2u=2sinucosu . Substitute sinu=−35 and cosu=45 ;

  sin2u=2(−35)(45)=−2425

Therefore sin2u=−2425

Apply double angle formula cos2u=cos2u−sin2u . Substitute sinu=−35 and cosu=45 ;

  cos2u=(45)2−(−35)2=1625−925=725

Therefore cos(2u)=725

Find tan(2u) using double angle formula; apply double angle formula for tangent

  tan2u=2tanu1−tan2u

Substitute; tanu=−34

  tan2u=2(−34)1−(−34)2=(−64716)=−64(167)=−247

Therefore;

  tan(2u)=−247 .

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Chapter 5, Problem 89RE
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Chapter 5, Problem 91RE

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

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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