`sin(theta) = -1/2` Find two solutions of each equation. Give your answers in degrees (0 <= theta <= 360) and radians (0 <= theta <= 2pi)

Textbook Question

Chapter 4, 4.4 - Problem 91b - Precalculus (3rd Edition, Ron Larson).
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nisarg's profile pic

nisarg | Student, Grade 11 | (Level 1) Valedictorian

Posted on

Sine and cosine at max are 1.  Cosine is X and Sine is Y. The values of them repeat as their graphs are waves. As you can see here 

 So here `7pi/6`  and `11pi/6`   can both equal theta

theta can be 210 degrees or it can be 330 degrees

kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

As wiggin42 stated is right 

`sin(theta) ` is negative so `theta` lies between `pi` to `2pi` or `180^@` to `360^@`

and

`sin(theta) = -1/2`

=> `theta = sin^-1(-1/2)`

`theta = 210 ^@ or 330^@ ` in degrees

and 

`theta = 7pi/6 or 11pi/6` in radians

the answer in radians was not given by wiggin42 .....so i gave the answer

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

`sin(theta)` is negative in the 3rd and 4th quadrants. Looking at a unit circle, `sin(theta) = -1/2` when `theta` equals 210 and 330 degrees. 

Sources:

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