What is $tan (arcsin (\frac{5}{6}))$ $tan(arcsin( 5/6))$ ?

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What is $tan (arcsin (\frac{5}{6}))$ $tan(arcsin( 5/6))$ ?

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Answer 1 · 2015-07-23T14:35:10

$tan (arcsin (\frac{5}{6})) = = \pm \frac{5}{\sqrt{11}}$ $tan(arcsin(5/6)) = =+-5/sqrt(11)$

Explanation:

If $x = arcsin (\frac{5}{6})$ $x = arcsin(5/6)$
$XXXX$ $color(white)("XXXX")$ then $sin (x) = \frac{5}{6}$ $sin(x) = 5/6$
and $x$ $x$ is one of the 2 possible angles indicated below
(arcsin is restricted to $[0, π]$ $[0,pi]$ ):
enter image source here

The third side ( $\pm \sqrt{11}$ $+-sqrt(11)$ ) can be derived using the Pythagorean theorem.

From the diagram:
$XXXX$ $color(white)("XXXX")$ $tan (x) = \pm \frac{5}{\sqrt{11}}$ $tan(x) = +-5/sqrt(11)$

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What is $tan (arcsin (\frac{5}{6}))$ $tan(arcsin( 5/6))$ ?

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