Question

Explain how to find the exact value of sin(570°).

Answer 1

Quick answer Sin(570) = - 1/2
Comment
570 as an angle contains 1 complete revolution of the terminal arm. The terminal arm begins at the origin and the other (in this case swings around until it records 570° turning around the x axis in an anticlockwise direction.

Anticlockwise means going from 12 o'clock to 9 o'clock to 6 o'clock then 3 o'clock and back to 12 o'clock.

What is 570° (∅) degrees equivalent to?
We keep on subtracting 360 until we get a number between 0 and 360 inclusive.

Written this way 0 ≤∅≤360
570 - 360 = 210°

So we need to find the equivalent of 210° 

Method
210° = 180° + 30°
This means that ∅ is 30° below the x axis in the 3rd quadrant.

Sin(30) = 1/2 
In the third quadrant, the sine is minus. so 
sin(210°) = - 1/2 <<<<<<< Answer 

Answer 2

For e2020 users:

Find that the terminal side lands in quadrant III.

The angle is coterminal with a 210° angle.

The reference angle is 30°.

The sine of 30° is 1/2.

Sine is negative in quadrant III.

The sine of 570° is –1/2.