คำตอบ - Trigonometry

Reflecting the number with respect to 360 degrees.

$$\sin \left(315°\right)=\sin \left(360-45°\right)$$

The period of trigonometric functions is 360 degrees.

$$\sin \left(360-45°\right)=\sin \left(360-45-360°\right)$$

Removing or simplifying the same numbers on the top and bottom of a fraction.

$$\sin \left(360-45-360°\right)=\sin \left(-45°\right)$$

Computing the sine of a negative angle.

$$\sin \left(-45°\right)=-\sin \left(45°\right)$$

Computing the sine of 45 degrees.

$$-\sin \left(45°\right)=-\frac{\sqrt{2}}{2}$$