Question

5

Select all the correct answers.

27

If the measure of angle 8 is 3, which statements are true?

The measure of the reference angle is 45°

sin(0) - 1/2

The measure of the reference angle is 60°

tan) = -V3

The measure of the reference angle is 30°

)

VS

cos(8) = Ž

-

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Answer 1

Correct statements are:

b.
`$\tan (\theta) = -√(3)$`

c. The measure of the reference angle is
`$60^(\circ)$`.

The measure of angle
`$\theta$` is
`$(2\pi)/(3)$`. This corresponds to a reference angle of
`$(\pi)/(3)$` because
`$(2\pi)/(3)$` is in the second quadrant.

Now, let's evaluate each statement:

a.
`$\sin (\theta) = -(1)/(2)$`

This is not true for
`$\theta = (2\pi)/(3)$`; the correct value is
`$\sin\left((2\pi)/(3)\right) = (√(3))/(2)$`.

b.
`$\tan (\theta) = -√(3)$`

This is true for
`$\theta = (2\pi)/(3)$`.

c. The measure of the reference angle is
`$60^(\circ)$`.

The reference angle is
`$(\pi)/(3)$`, which is equivalent to
`$60^(\circ)$`. This statement is true.

d. The measure of the reference angle is
`$30^(\circ)$`.

This is not true; the correct measure is
`$60^(\circ)$`.

e. The measure of the reference angle is
`$45^(\circ)$`.

This is not true; the correct measure is
`$60^(\circ)$`.

f.
`$\cos (\theta) = (√(3))/(2)$`

This is not true for
`$\theta = (2\pi)/(3)$`; the correct value is
`$\cos\left((2\pi)/(3)\right) = -(1)/(2)$`.

Complete Question:

Select all the correct answers.

If the measure of angle
`$\theta$` is
`$(2 \pi)/(3)$`, which statements are true?

a.
`$\sin (\theta)=-(1)/(2)$`

b.
`$\tan (\theta)=-√(3)$`

c. The measure of the reference angle is
`$60^(\circ)$`.

d. The measure of the reference angle is
`$30^(\circ)$`.

e. The measure of the reference angle is
`$45^(\circ)$`.

f.
`$\cos (\theta)=(√(3))/(2)$`