Key to "What is the exact value of cos⁡135 ?"

Kathy Williams

Answered question

2021-12-12

What is the exact value of

\cos 135

aquariump9

Beginner2021-12-13Added 40 answers

Explanation:

{\cos 135}^{\circ} = \cos (45^{\circ} + 90^{\circ}) = - {\cos 45}^{\circ} = - \frac{1}{\sqrt{2}}

{\cos 135}^{\circ} = \cos (180^{\circ} - 45^{\circ}) = - {\cos 45}^{\circ} = - \frac{1}{\sqrt{2}}

Lakisha Archer

Beginner2021-12-14Added 39 answers

Cos 135° is an angle in the second quadrant.
In the second quadrant, cos is negative.

\cos θ = \frac{x}{r}

\cos 135 = \cos (180 - 45) = - {\cos 45}^{\circ}

An angle of

45^{\circ}

is found ina a right-angled triangle of sides

1 : 1 : \sqrt{2}

{\cos 45}^{\circ} = \frac{1}{\sqrt{2}}

{\cos 135}^{\circ} = - {\cos 45}^{\circ} = - \frac{1}{\sqrt{2}}

Note that

\sqrt{2}

is an irrational number and cannot be given as an exact decimal.

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