How do you calculate the $arcsin (- \frac{1}{\sqrt{2}})$ $arcsin (-1/ sqrt 2)$ ?

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How do you calculate the $arcsin (- \frac{1}{\sqrt{2}})$ $arcsin (-1/ sqrt 2)$ ?

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Answer 1 · 2015-11-27T21:17:05

Calculate $arcsin (- \frac{1}{\sqrt{2}})$ $arcsin (-1/sqrt2)$

Ans: $\frac{5 π}{4} and \frac{7 π}{4}$ $(5pi)/4 and (7pi)/4$

Explanation:

Unit circle and trig table of special arcs -->
$sin x = - \frac{1}{\sqrt{2}} = - \frac{\sqrt{2}}{2}$ $sin x = - 1/sqrt2 = - sqrt2/2$ --> $a r c x = - \frac{π}{4}$ $arc x = - pi/4$
Unit circle gives another arc x that has the same sine value:
$x = π + \frac{π}{4} = 5 \frac{π}{4} .$ $x = pi + pi/4 = 5pi/4.$
Ans: $x = \frac{5 π}{4}$ $x = (5pi)/4$ , and $x = \frac{7 π}{4}$ $x = (7pi)/4$ (or -pi/4)

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How do you calculate the $arcsin (- \frac{1}{\sqrt{2}})$ $arcsin (-1/ sqrt 2)$ ?

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