Trigonometry Examples

$\tan (990)$

Step 1

Rewrite $\tan (990)$ in terms of sines and cosines.

$\frac{\sin (990)}{\cos (990)}$

Step 2

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

$\frac{\sin (990)}{\cos (270)}$

Step 3

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 third quadrant.

$\frac{\sin (990)}{- \cos (90)}$

Step 4

The exact value of $\cos (90)$ is $0$ .

$\frac{\sin (990)}{- 0}$

Step 5

Multiply $- 1$ by $0$ .

$\frac{\sin (990)}{0}$

Step 6

The expression contains a division by $0$ . The expression is undefined.

Undefined