Question

When Θ = 5 pi over 3, what are the reference angle and the sign values for sine, cosine, and tangent?

Answer 1

Θ = 5 pi/3
5pi/3 lies in quadrant IV = 2pi - pi/3
The reference angle is pi/3

Θ'= pi over 3, cosine is positive, sine and tangent are negative

Answer 2

the reference angle is given by
`(\pi)/(3)`

sine = negative

cosine = positive

tangent = negative

Explanation:

We have been given the angle
`\theta=(5\pi)/(3)`

The angle lies in Quadrant IV. Hence, in order to find the reference angle, we can subtract this angle with
`2\pi`

Therefore, the reference angle is given by

`2\pi - (5\pi)/(3) \\\\=(\pi)/(3)`

In Quadrant IV, cosine and secant functions are positive and rest trigonometric functions are negative.

Thus, we have

sine = negative

cosine = positive

tangent = negative