How do you evaluate $arcsin (\frac{\sqrt{2}}{2})$ $arcsin(sqrt2/2)$ without a calculator?

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How do you evaluate $arcsin (\frac{\sqrt{2}}{2})$ $arcsin(sqrt2/2)$ without a calculator?

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Answer 1 · 2017-02-13T14:33:20

$\frac{π}{4} + 2 k π$ $pi/4 + 2kpi$
$\frac{3 π}{4} + 2 k π$ $(3pi)/4 + 2kpi$

Explanation:

Use trig table and unit circle:
$sin x = \frac{\sqrt{2}}{2}$ $sin x = sqrt2/2$ --> trig table gives --> arc $x = \frac{π}{4}$ $x = pi/4$ .
Unit circle gives another arc x that has the same sin value:
$x = (π - \frac{π}{4}) = \frac{3 π}{4}$ $x = (pi - pi/4) = (3pi)/4$ .
General answers:
$x = \frac{π}{4} + 2 k π$ $x = pi/4 + 2kpi$
$x = (3 π) 4 + 2 k π$ $x = (3pi)4 + 2kpi$

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