Question

Select all angle measures for which sin\theta =-(\sqrt(2))/(2) (3\pi )/(4) (5\pi )/(4) (7\pi )/(4) (9\pi )/(4) (13\pi )/(4)

Answer 1

(b) 5π/2

(c) 7π/2

(e) 13π/2

Explanation:

You want the angles in the list where sin(θ) is -√2/2.

Sine

The sine function is negative for angles in the 3rd and 4th quadrants. The magnitude is √2/2 for angles whose reference angle is π/4. These angles are ...

5π/4, 7π/4, 13π/4, 15π/4

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Additional comment

Adding √2/2 to the given equation makes it ...

sin(θ) + √2/2 = 0

The solutions will be found at the x-intercepts of sin(θ) + √2/2 as shown in the attached graph.

The sine is the y-coordinate of points on the unit circle. In the second attachment, you will notice that the coordinates are (•, -√2/2) for angles 5π/4 and 7π/4. Adding 2π = 8π/4 to these values gets the next pair of angles with the right sine value.