How do you find the value of $arccos (- \frac{\sqrt{2}}{2})$ $arccos(-sqrt2/2)$ ?

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How do you find the value of $arccos (- \frac{\sqrt{2}}{2})$ $arccos(-sqrt2/2)$ ?

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Answer 1 · 2018-02-12T13:33:53

The value is $\frac{3 π}{4}$ $(3pi)/4$

Explanation:

Given ${cos}^{- 1} (- \frac{\sqrt{2}}{2}) = π - {cos}^{- 1} (\frac{\sqrt{2}}{2}) (\frac{\sqrt{2}}{\sqrt{2}})$ $cos^-1(-sqrt2/2)=pi-cos^-1(sqrt2/2)(sqrt2/sqrt2)$
$\Rightarrow π - {cos}^{- 1} (\frac{1}{\sqrt{2}}) \Rightarrow π - \frac{π}{4} \Rightarrow \frac{3 π}{4}$ $rArrpi-cos^-1(1/sqrt2)rArrpi-pi/4rArr(3pi)/4$

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How do you find the value of $arccos (- \frac{\sqrt{2}}{2})$ $arccos(-sqrt2/2)$ ?

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How do you find the value of $arccos (- \frac{\sqrt{2}}{2})$ $arccos(-sqrt2/2)$ ?