Trigonometry Examples

$\tan (- 315)$

Step 1

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

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

Step 2

Apply the tangent half-angle identity.

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Multiply $- 1$ by $0$ .

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

Step 4.4

Add $1$ and $0$ .

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

Step 4.5

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

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

Step 4.6

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

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

Step 4.7

Add $1$ and $0$ .

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

Step 4.8

Divide $1$ by $1$ .

$\sqrt{1}$

Step 4.9

Any root of $1$ is $1$ .

$1$