`cos(theta) = sqrt(2)/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 92a - 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 `pi/4`   and `7pi/4`   can both equal theta

theta can be 45 degrees or it can be 315 degrees

kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

`cos(theta)`  is positive in the 1st and 4th quadrants. 

and

`cos(theta) = -sqrt(2)/2 = 1/sqrt(2)`

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

`theta = 45 ^@ or 315^@ ` in degrees

and 

`theta = pi/4 or (7pi)/4` in radians

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

`cos(theta)` is positive in the 1st and 4th quadrants. Looking at a unit circle, the values of theta that satisfy these conditions are 45 and 315 degrees. 

Sources:

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