   Chapter T, Problem 6DDT ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# If sin x = 1 3 and sec y = 5 4 , where x and y lie between 0 and π/2, evaluate sin(x + y).

To determine

To evaluate: The value of sin(x+y).

Explanation

Given:

The values are sinx=13andsecy=54, where x and y lie between 0 and π2.

Formula used:

1. 1. sin2x+cos2x=1
2. 2. sin(x+y)=sinxcosy+cosxsiny

Calculation:

Consider the value sinx=13.

Use the above mentioned formula 1 and find the value of cosx as follows,

Substitute sinx=13 in cosx=1sin2x,

cosx=1(13)2=119=89=223

Consider the value secy=54

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