Trigonometry Examples

$\tan (135 °)$

Step 1

Find the value using the definition of tangent.

$\tan (135 °) = \frac{opposite}{adjacent}$

Step 2

Substitute the values into the definition.

$\tan (135 °) = \frac{\frac{\sqrt{2}}{2}}{- \frac{\sqrt{2}}{2}}$

Step 3

Simplify the result.

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Step 3.1

Cancel the common factor of $\frac{\sqrt{2}}{2}$ .

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Step 3.1.1

Cancel the common factor.

$\frac{\frac{\sqrt{2}}{2}}{- \frac{\sqrt{2}}{2}}$

Step 3.1.2

Rewrite the expression.

$\frac{1}{- 1}$

Step 3.1.3

Move the negative one from the denominator of $\frac{1}{- 1}$ .

$- 1 \cdot 1$

Step 3.2

Multiply $- 1$ by $1$ .

$- 1$

Step 4