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Find the value of tan(sin^-1(1/2))

Find the value of tan(sin^-1(1/2))-example-1
User Rphv
by
6.7k points

2 Answers

2 votes

If you know that
\sin\frac\pi3=\frac12, then you know right away


\tan\left(\sin^(-1)\frac12\right)=\tan\frac\pi3=\frac1{\sqrt}3=\frac{\sqrt3}3

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Otherwise, you can derive the same result. Let
\theta=\sin^(-1)\frac12, so that
\sin\theta=\frac12.
\sin^(-1) is bounded, so we know
-\frac\pi2\le\theta\le\frac\pi2. For these values of
\theta, we always have
\cos\theta\ge0.

So, recalling the Pythagorean theorem, we find


\cos^2\theta+\sin^2\theta=1\implies\cos\theta=√(1-\sin^2\theta)=√(1-\left(\frac12\right)^2)=\frac{\sqrt3}2

Then


\tan\theta=\tan\left(\sin^(-1)\frac12\right)=(\sin\theta)/(\cos\theta)=\frac{\frac12}{\frac{\sqrt3}2}=\frac1{\sqrt3}=\frac{\sqrt3}3

as expected.

User Kyanna
by
7.4k points
5 votes

Answer:

c. square root 3/3

Explanation:

just did it on edg

User Max Rogers
by
6.9k points