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kari74 [83]
3 years ago
10

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

Mathematics
2 answers:
suter [353]3 years ago
5 0

If you know that \sin\dfrac\pi3=\dfrac12, then you know right away

\tan\left(\sin^{-1}\dfrac12\right)=\tan\dfrac\pi3=\dfrac1{\sqrt}3=\dfrac{\sqrt3}3

###

Otherwise, you can derive the same result. Let \theta=\sin^{-1}\dfrac12, so that \sin\theta=\dfrac12. \sin^{-1} is bounded, so we know -\dfrac\pi2\le\theta\le\dfrac\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=\sqrt{1-\sin^2\theta}=\sqrt{1-\left(\dfrac12\right)^2}=\dfrac{\sqrt3}2

Then

\tan\theta=\tan\left(\sin^{-1}\dfrac12\right)=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}=\dfrac{\sqrt3}3

as expected.

____ [38]3 years ago
3 0

Answer:

c. square root 3/3

Step-by-step explanation:

just did it on edg

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Answer:

5 and 1/3 cups of water.

Step-by-step explanation:

Set up a proportion like this:

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Set up an equation so that the proportions equal each other. It helps if you write them in fraction form:

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Use cross multiplication to get the new equation:

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Then, divide both sides by 3 to get the amount for w, or water, by itself:

5 and 1/3 = w

I hope this helps! ☺

8 0
2 years ago
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Answer:

1.80m + 3 ≤ 25

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Jennifer only has $25 to spend, so she can't spend any more than 25. This means that the money she can spend must be less than or equal to $25:

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side^2 = [60 * 4 * tan (36)] / 5

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