What is the exact value of $Cos 135$ ?

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Answer 1 · 2015-05-10T03:02:36

$cos 135° = -1/sqrt2$

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

or

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

Answer 2 · 2016-05-12T21:54:53

$cos 135° = - cos 45° =- 1/sqrt2$

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.

What is the exact value of Cos 135Cos 135?