Question

Let theta be and angle in quadrant IV that has reference pi/3. What is sin(theta)?

Answer 1

Given:

`\theta` is an angle in quadrant IV that has reference
`(\pi)/(3)`.

To find:

The value of
`\sin \theta`.

Solution:

We know that only cos and sec are positive in quadrant IV and all other trigonometric ratios are negative in quadrant IV.

Since
`\theta` is an angle in quadrant IV that has reference
`(\pi)/(3)`, therefore the value of
`\sin \theta` must be negative.

`\sin \theta=-\sin (\pi)/(3)`

`\sin \theta=-(√(3))/(2)`

Therefore, the required value is
`\sin \theta=-(√(3))/(2)`.