Precalculus Examples

tan (- 315)

$\tan (- 315)$

Step 1

Rewrite

- 315

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

2

$2$ .

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

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

Step 2

Apply the tangent half-angle identity.

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

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

Step 3

Change the

\pm

$\pm$ to

+

$+$ because tangent is positive in the first quadrant.

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

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

Step 4

Simplify

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

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

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Step 4.1

Add full rotations of

360

$360$ ° until the angle is between

0

$0$ ° and

360

$360$ °.

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

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

Step 4.2

The exact value of

cos (90)

$\cos (90)$ is

0

$0$ .

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

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

Step 4.3

Multiply

- 1

$- 1$ by

0

$0$ .

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

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

Step 4.4

Add

1

$1$ and

0

$0$ .

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

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

Step 4.5

Add full rotations of

360

$360$ ° until the angle is between

0

$0$ ° and

360

$360$ °.

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

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

Step 4.6

The exact value of

cos (90)

$\cos (90)$ is

0

$0$ .

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

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

Step 4.7

Add

1

$1$ and

0

$0$ .

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

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

Step 4.8

Divide

1

$1$ by

1

$1$ .

\sqrt{1}

$\sqrt{1}$

Step 4.9

Any root of

1

$1$ is

1

$1$ .

1

$1$

1

$1$