Trigonometry Examples

$\cot (- 315 °)$

Step 1

Rewrite $- 315 °$ as an angle where the values of the six trigonometric functions are known divided by $2$ .

$\cot (\frac{- 630}{2})$

Step 2

Apply the reciprocal identity.

$\frac{1}{\tan (\frac{- 630}{2})}$

Step 3

Apply the tangent half-angle identity.

$\frac{1}{\pm \sqrt{\frac{1 - \cos (- 630)}{1 + \cos (- 630)}}}$

Step 4

Change the $\pm$ to $+$ because cotangent is positive in the first quadrant.

$\frac{1}{\sqrt{\frac{1 - \cos (- 630)}{1 + \cos (- 630)}}}$

Step 5

Simplify $\frac{1}{\sqrt{\frac{1 - \cos (- 630)}{1 + \cos (- 630)}}}$ .

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Step 5.1

Simplify the numerator.

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Step 5.1.1

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

$\frac{1}{\sqrt{\frac{1 - \cos (90)}{1 + \cos (- 630)}}}$

Step 5.1.2

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

$\frac{1}{\sqrt{\frac{1 - 0}{1 + \cos (- 630)}}}$

Step 5.1.3

Multiply $- 1$ by $0$ .

$\frac{1}{\sqrt{\frac{1 + 0}{1 + \cos (- 630)}}}$

Step 5.1.4

Add $1$ and $0$ .

$\frac{1}{\sqrt{\frac{1}{1 + \cos (- 630)}}}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

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

$\frac{1}{\sqrt{\frac{1}{1 + \cos (90)}}}$

Step 5.2.2

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

$\frac{1}{\sqrt{\frac{1}{1 + 0}}}$

Step 5.2.3

Add $1$ and $0$ .

$\frac{1}{\sqrt{\frac{1}{1}}}$

Step 5.3

Simplify the denominator.

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Step 5.3.1

Divide $1$ by $1$ .

$\frac{1}{\sqrt{1}}$

Step 5.3.2

Any root of $1$ is $1$ .

$\frac{1}{1}$

Step 5.4

Divide $1$ by $1$ .

$1$