# The value of sin ( x + y ) .

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter T, Problem 6DDT
To determine

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

Expert Solution

The value of sin(x+y) is 115(4+62).

### Explanation of Solution

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.

That is, cosy=45

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

Substitute cosy=45 in siny=1cos2y,

siny=1(45)2=11625=925=35

Use the above mentioned formula 2 and find the value of sin(x+y) as follows,

Substitute cosx=223andsiny=35 in sin(x+y)=sinxcosy+cosxsiny,

sin(x+y)=13×45+223×35=415+6215=115(4+62)

Thus, the value of sin(x+y) is 115(4+62).

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