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3 years ago

13

If angle P measures 60 degrees , what is the measure of angle c?

1 answer:

Mashutka [201]3 years ago

5 0

Answer:

120 degrees

Step-by-step explanation:

Hope this helped, Have a Great Day!!

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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

Read 2 more answers

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VMariaS [17]

Answer:

$\frac{1625z^{10}}{x^{5}}$

Step-by-step explanation:

We want to simplify:

$\frac{13x^{-5}y^0}{5^{-3}z^{-10}}$

We rewrite as positive index to get:

$\frac{13y^05^{3}z^{10}}{x^{5}}$

This simplifies to

$\frac{13*1*125z^{10}}{x^{5}}$

This will finally give us:

$\frac{1625z^{10}}{x^{5}}$

We cannot simplify further.

Hence the simplest form is $\frac{1625z^{10}}{x^{5}}$

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