คำตอบ - Trigonometry

The period of trigonometric functions is 360 degrees.

$$\sin \left(510°\right)=\sin \left(510-360°\right)$$

Subtracting one integer from another.

$$\sin \left(510-360°\right)=\sin \left(150°\right)$$

Reflecting the number with respect to 360 degrees.

$$\sin \left(150°\right)=\sin \left(180-30°\right)$$

Reflecting the sine function with respect to 180 degrees.

$$\sin \left(180-30°\right)=\sin \left(30°\right)$$

Computing the sine of 30 degrees.

$$\sin \left(30°\right)=\frac{1}{2}$$