Trigonometry Examples

$\sin (θ) = 0$ , $\sec (θ) = - 1$

Step 1

To find the value of $\cos (θ)$ , use the fact that $\frac{1}{\sec (θ)}$ then substitute in the known values.

$\cos (θ) = \frac{1}{\sec (θ)} = \frac{1}{- 1}$

Step 2

Divide $1$ by $- 1$ .

$\cos (θ) = \frac{1}{\sec (θ)} = - 1$

Step 3

To find the value of $\tan (θ)$ , use the fact that $\tan (θ) = \frac{\sin (θ)}{\cos (θ)}$ then substitute in the known values.

$\tan (θ) = \frac{\sin (θ)}{\cos (θ)} = \frac{0}{- 1}$

Step 4

Divide $0$ by $- 1$ .

$\tan (θ) = \frac{\sin (θ)}{\cos (θ)} = 0$

Step 5

To find the value of $\cot (θ)$ , use the fact that $\frac{1}{\tan (θ)}$ then substitute in the known values.

$\cot (θ) = \frac{1}{\tan (θ)} = \frac{1}{0}$

Step 6

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

Undefined

Step 7

To find the value of $\csc (θ)$ , use the fact that $\frac{1}{\sin (θ)}$ then substitute in the known values.

$\csc (θ) = \frac{1}{\sin (θ)} = \frac{1}{0}$

Step 8

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

Undefined

Step 9

The trig functions found are as follows:

Undefined