Question

V3

The angle 01 is located in Quadrant III, and sin(01) =

2

What is the value of cos(01)?

Express your answer exactly.

Answer 1

Question:

The angle
`\theta_1` is located in Quadrant III, and
`sin(\theta_1) = - \sqrt{(3)/(2)}`.

What is the value of
`cos(\theta_1)` ?

Express your answer exactly.
`cos(\theta1) =` ________

Answer:

`cos(\theta_1) = - (1)/(2)`

Explanation:

Given:

`sin(\theta_1) = - \sqrt{(3)/(2)}`

Since the angle
`\theta_1` is located in Quadrant III, we have:

`sin(\theta_1) = sin(\pi + (\pi)/(3))`

`\theta_1 = \pi + (\pi)/(3)`

`\theta_1 = (4 \pi)/(3)`

Thus,
`cos(\theta_1)` =

`cos(\theta_1) = cos(\pi + (\pi)/(3))`

`cos(\theta_1) = -cos((\pi)/(3))`

`cos(\theta_1) = - (1)/(2)`