Question

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
sin(θ) = − sqrt2/2

Answer 1

Answer:

225°, 315°

Step-by-step explanation:

Given:

$\sin \theta = -\frac{\sqrt{2}}{2}$

Here, the sine value is negative. So, we know that, sine is negative in the third and fourth quadrant of the unit circle.

Therefore, we will get two values for $\theta$ between (180°, 360°).

Solving for $\theta$ we take inverse of sine.

$\theta = \sin^{-1}(-\frac{\sqrt{2}}{2})$

From the unit circle below, we conclude that the angle for the given sine value are 225° and 315°.

Therefore, the solutions are $\theta =$ 225°, 315°.