Trigonometry Examples

cos (135 °)

$\cos (135 °)$

Step 1

Find the value using the definition of cosine.

cos (135 °) = \frac{adjacent}{hypotenuse}

$\cos (135 °) = \frac{adjacent}{hypotenuse}$

Step 2

Substitute the values into the definition.

cos (135 °) = \frac{- \frac{\sqrt{2}}{2}}{1}

$\cos (135 °) = \frac{- \frac{\sqrt{2}}{2}}{1}$

Step 3

Divide

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

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

1

$1$ .

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

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

Decimal Form:

- 0.70710678 \dots

$- 0.70710678 \dots$

Step 5

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$