Trigonometry Examples

sin (θ) = - 1

$\sin (θ) = - 1$ ,

cot (θ) = 0

$\cot (θ) = 0$

Step 1

To find the value of

tan (θ)

$\tan (θ)$ , use the fact that

\frac{1}{cot (θ)}

$\frac{1}{\cot (θ)}$ then substitute in the known values.

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

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

Step 2

The expression contains a division by

0

$0$ . The expression is undefined.

Undefined

Step 3

To find the value of

cos (θ)

$\cos (θ)$ , use the fact that

tan (θ) = \frac{sin (θ)}{cos (θ)}

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

cos (θ) = \frac{sin (θ)}{tan (θ)}

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

$\sec (θ)$ , use the fact that

\frac{1}{cos (θ)}

$\frac{1}{\cos (θ)}$ 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

$1$ and

- 1

$- 1$ .

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Step 6.1.1

Rewrite

1

$1$ as

- 1 (- 1)

$- 1 (- 1)$ .

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

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

Step 6.1.2

Move the negative in front of the fraction.

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

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

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

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

Step 6.2

Multiply the numerator by the reciprocal of the denominator.

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

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

Step 6.3

Multiply

Undefined

$Undefined$ by

1

$1$ .

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

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

Undefined

Step 7

To find the value of

csc (θ)

$\csc (θ)$ , use the fact that

\frac{1}{sin (θ)}

$\frac{1}{\sin (θ)}$ then substitute in the known values.

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

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

Step 8

Divide

1

$1$ by

- 1

$- 1$ .

csc (θ) = \frac{1}{sin (θ)} = - 1

$\csc (θ) = \frac{1}{\sin (θ)} = - 1$

Step 9

The trig functions found are as follows:

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