Question

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

Answer 1

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.

Answer 2

Answer:

-1/2

Step-by-step explanation:

Start by subtracting 360° from 570°, obtaining 210°.  These two angles share the same terminal side, located in Quadrant III, and thus share their trig function values.

Similarly, subtract 180° from 210°, obtaining 30°.  In Quadrant III, the opposite side is -1, the adjacent side is -√3/2 and the hypotenuse is 2.

The sine of 570° is thus opp/hyp, or -1/2.