Question

Select all angle measures for which sin theta= -sqrt2/2

3pi/4
5pi/4
7pi/4
9pi/4
13pi/4

Answer 1

5pi/4
7pi/4
13pi/4
Those are the answers to your question have a nice day

Answer 2

There are only two possible values that will give sin(θ)=-(√2)/2 which are 5π/4 and 7π/4.

What is an angle?

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

The value of theta is given as,

Sin(θ) = -√2/2

θ = Sin⁻¹(-√2/2)

θ = -45° = -(π/4)

Now, the angle of -45° is possible only when the value of x is negative or y is negative.

• If the value of x is negative, then the angle can be written as,

         θ = π+(π/4) = 5π/4

• If the value of y is negative, then the angle can be written as,

        θ = 3π/2 + (π/4) = 7π/4

Hence, there are only two possible values that will give sin(θ)=-(√2)/2 which are 5π/4 and 7π/4.

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