Trigonometry Examples

$\sin (θ) = - 1$ , $\cot (θ) = 0$

Step 1

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

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

Step 2

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

Undefined

Step 3

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

Undefined

Step 4

Move the negative in front of the fraction.

Undefined

Step 5

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

Undefined

Step 6

Simplify the result.

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Step 6.1

Cancel the common factor of $1$ and $- 1$ .

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Step 6.1.1

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 6.1.2

Move the negative in front of the fraction.

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

Step 6.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 6.3

Multiply $Undefined$ by $1$ .

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

Undefined

Step 7

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

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

Step 8

Divide $1$ by $- 1$ .

$\csc (θ) = \frac{1}{\sin (θ)} = - 1$

Step 9

The trig functions found are as follows:

Undefined