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2 years ago

Sin (a/2) = + or - sqrt 1-cos a / 2 for all values of a. A. True B. False

Mathematics

1 answer:

loris [4]2 years ago

8 0

False, I think that’s correct but I’m sorry if bot.

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

suter [353]

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

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

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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.

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3 years ago

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sukhopar [10]

Answer:

point a is positive but point b is negative

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2 years ago

Use the distributive property to write an equivalent expression in simplest form.<br> 9(4h+ 9m)

sammy [17]

Answer:

36h+81m

Step-by-step explanation:

9*4h+9*9m=36h+81m

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How high did Abby climb above their original starting<br> position?

PIT_PIT [208]

Idk what are the possible answers

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A bakery makes donuts at the rate of 225 per hour. How long will it take the bakery to fill an order of 500 donuts?

dem82 [27]

If I understood your question properly, it would take 2 hours for the company to fill an order of 500 donuts.

I hope you found this helpful! C:

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