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Chapter 7: Q. 70 (page 504)

Solve the equation on the interval 0鈮�胃鈮�2蟺.

role="math" localid="1646734122417" sin胃+sin2胃=0

Short Answer

Expert verified

On solving the equation, we get,

0,2蟺3,蟺,4蟺3

Step by step solution

01

Step 1. Given information.

Consider the given question,

sin胃+sin2胃=00鈮�胃鈮�2蟺

We know, sin2胃=2sin胃路cos胃,

sin胃+2sin胃cos胃=0sin胃1+2cos胃=0

Then,

sin胃=0

Also,

1+2cos胃=0cos胃=-12

02

Step 2. Solve the equation for the given interval.

Consider the given question,

sin胃=0cos胃=-120鈮�胃鈮�2蟺

Solving sin胃for the interval 0鈮�胃鈮�2蟺,

sin胃=0胃=sin-10胃=0,蟺

Solving cos胃=-12for the interval 0鈮�胃鈮�2蟺,

cos胃=-12胃=cos-1-12胃=2蟺3,4蟺3

Therefore, the solution set is 胃鈭�0,2蟺3,蟺,4蟺3.

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