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

225°, 315°

Explanation:

Given:

`\sin \theta = -(√(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)(-(√(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°.