Question

What is the exact value of `Cos 135`?

Answer 1

`cos 135° = -1/sqrt2`

Explanation:

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

or

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

Answer 2

`cos 135° = - cos 45° =- 1/sqrt2`

Explanation:

Cos 135° is an angle in the second quadrant.

In the second quadrant, cos is negative. `Cos theta = x/r`

`Cos 135 = cos(180-45) = -cos 45°`

An angle of `45°` is found in a right-angled triangle of sides `1 : 1 : sqrt2`

`Cos 45° = 1/sqrt2`

`:. cos 135° = - cos 45° = -1/sqrt2`

Note that `sqrt2` is an irrational number and cannot be given as an exact decimal.