How do you find the value of $tan (arcsin (\frac{1}{2}))$ $tan(arcsin(1/2))$ ?

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How do you find the value of $tan (arcsin (\frac{1}{2}))$ $tan(arcsin(1/2))$ ?

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Answer 1 · 2016-08-02T05:08:42

$- \frac{\sqrt{3}}{3} and \frac{\sqrt{3}}{3}$ $-sqrt3/3 and sqrt3/3$

Explanation:

Trig table of special arcs, and trig unit circle -->
sin x = 1/2 --> arc $x = \frac{π}{6}$ $x = pi/6$ , and arc $x = \frac{5 π}{6}$ $x = (5pi)/6$

a. $x = \frac{π}{6} - \to tan x = \frac{\sqrt{3}}{3}$ $x = pi/6 --> tan x = sqrt3/3$
b. $x = \frac{5 π}{6} - \to tan x = - \frac{\sqrt{3}}{3}$ $x = (5pi)/6 --> tan x = -sqrt3/3$

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How do you find the value of $tan (arcsin (\frac{1}{2}))$ $tan(arcsin(1/2))$ ?

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