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

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### 3 Answers

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

`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**

`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.

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