What is the exact value of #Cos 135#?

2 Answers
May 10, 2015

Answer:

#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

Answer:

#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.