# What is the exact value of \cos135 ?

Kathy Williams 2021-12-12 Answered
What is the exact value of $\mathrm{cos}135$ ?
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## Expert Answer

aquariump9
Answered 2021-12-13 Author has 40 answers
Explanation:
${\mathrm{cos}135}^{\circ }=\mathrm{cos}\left({45}^{\circ }+{90}^{\circ }\right)=-{\mathrm{cos}45}^{\circ }=-\frac{1}{\sqrt{2}}$
or
${\mathrm{cos}135}^{\circ }=\mathrm{cos}\left({180}^{\circ }-{45}^{\circ }\right)=-{\mathrm{cos}45}^{\circ }=-\frac{1}{\sqrt{2}}$
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Lakisha Archer
Answered 2021-12-14 Author has 39 answers
Cos 135° is an angle in the second quadrant.
In the second quadrant, cos is negative. $\mathrm{cos}\theta =\frac{x}{r}$
$\mathrm{cos}135=\mathrm{cos}\left(180-45\right)=-{\mathrm{cos}45}^{\circ }$
An angle of ${45}^{\circ }$ is found ina a right-angled triangle of sides $1:1:\sqrt{2}$
${\mathrm{cos}45}^{\circ }=\frac{1}{\sqrt{2}}$
${\mathrm{cos}135}^{\circ }=-{\mathrm{cos}45}^{\circ }=-\frac{1}{\sqrt{2}}$
Note that $\sqrt{2}$ is an irrational number and cannot be given as an exact decimal.
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