Trigonometry Examples

$\sin (- 390) + \cos (495)$

Step 1

Add full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$\sin (330) + \cos (495)$

Step 2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

$- \sin (30) + \cos (495)$

Step 3

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$- \frac{1}{2} + \cos (495)$

Step 4

Remove full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$- \frac{1}{2} + \cos (135)$

Step 5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$- \frac{1}{2} - \cos (45)$

Step 6

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

$- \frac{1}{2} - \frac{\sqrt{2}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2} - \frac{\sqrt{2}}{2}$

Decimal Form:

$- 1.20710678 \dots$