Trigonometry Examples

tan (- \frac{π}{2})

$\tan (- \frac{π}{2})$

Step 1

Rewrite

tan (- \frac{π}{2})

$\tan (- \frac{π}{2})$ in terms of sines and cosines.

\frac{sin (- \frac{π}{2})}{cos (- \frac{π}{2})}

$\frac{\sin (- \frac{π}{2})}{\cos (- \frac{π}{2})}$

Step 2

Add full rotations of

2 π

$2 π$ until the angle is greater than or equal to

0

$0$ and less than

2 π

$2 π$ .

\frac{sin (- \frac{π}{2})}{cos (\frac{3 π}{2})}

$\frac{\sin (- \frac{π}{2})}{\cos (\frac{3 π}{2})}$

Step 3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

\frac{sin (- \frac{π}{2})}{cos (\frac{π}{2})}

$\frac{\sin (- \frac{π}{2})}{\cos (\frac{π}{2})}$

Step 4

The exact value of

cos (\frac{π}{2})

$\cos (\frac{π}{2})$ is

0

$0$ .

\frac{sin (- \frac{π}{2})}{0}

$\frac{\sin (- \frac{π}{2})}{0}$

Step 5

The expression contains a division by

0

$0$ . The expression is undefined.

Undefined