BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter C, Problem 28E
To determine

To calculate:

The value of following expression:

  cos2y

Expert Solution

Answer to Problem 28E

The given expression cos2y is evaluated as 725 .

Explanation of Solution

Given information:

  sinx=13secy=540x,yπ2

Formula Used:

  cos2θ=2cos2θ1

Calculation:

Know that:

  secx=hypotenusadjecentsecx=54

Need to sketch the triangle for secx :

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter C, Problem 28E

Fig. 2 Triangle for secx

So, hypotenuse is equal to 5 and the length of the adjacent side is equal to 4 . So, use the Pythagoras theorem:

  r2=opposite2+a252=opposite2+42opposite2=9opposite=3

And the remaining side opposite to y is 3 . :

  siny=35cosy=1secy=45

Now, evaluate the given expression as:

  cos2y=2cos2y1cos2y=2(45)21cos2y=2(1625)(2525)cos2y=(3225)(2525)cos2y=322525cos2y=725

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