คำตอบ - Trigonometry

The period of trigonometric functions is 360 degrees.

$$\cos \left(585°\right)=\cos \left(585-360°\right)$$

Subtracting one integer from another.

$$\cos \left(585-360°\right)=\cos \left(225°\right)$$

Reflecting the number with respect to 360 degrees.

$$\cos \left(225°\right)=\cos \left(360-135°\right)$$

The period of trigonometric functions is 360 degrees.

$$\cos \left(360-135°\right)=\cos \left(360-135-360°\right)$$

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

$$\cos \left(360-135-360°\right)=\cos \left(-135°\right)$$

Computing the cosine of a negative angle.

$$\cos \left(-135°\right)=\cos \left(135°\right)$$

Reflecting the number with respect to 360 degrees.

$$\cos \left(135°\right)=\cos \left(180-45°\right)$$

Reflecting the cosine function with respect to 180 degrees.

$$\cos \left(180-45°\right)=-\cos \left(45°\right)$$

Computing the cosine of 45 degrees.

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