# What is the exact value of Cos 135?

May 10, 2015

cos 135° = -1/sqrt2

#### Explanation:

cos 135° = cos (45° + 90°) = - cos 45° = - 1/(sqrt2)

or

cos 135° = cos (180°-45°) = - cos 45° = - 1/(sqrt2)

May 12, 2016

cos 135° = - cos 45° =- 1/sqrt2

#### Explanation:

Cos 135° is an angle in the second quadrant.

In the second quadrant, cos is negative. $C o s \theta = \frac{x}{r}$

Cos 135 = cos(180-45) = -cos 45°

An angle of 45° is found in a right-angled triangle of sides $1 : 1 : \sqrt{2}$

Cos 45° = 1/sqrt2

:. cos 135° = - cos 45° = -1/sqrt2

Note that $\sqrt{2}$ is an irrational number and cannot be given as an exact decimal.