3 years ago

What is the distance between these two points

Mathematics

1 answer:

irakobra [83]3 years ago

7 0

Answer:

pretty sure it is 11

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Please help me <br><br>If 180°<α<270°, cos⁡ α=−8/17, what is sin -α?

rewona [7]

Starting from the fundamental trigonometric equation, we have

$\cos^2(\alpha)+\sin^2(\alpha)=1 \iff \sin(\alpha)=\pm\sqrt{1-\cos^2(\alpha)}$

Since $180$ , we know that the angle lies in the third quadrant, where both sine and cosine are negative. So, in this specific case, we have

$\sin(\alpha)=-\sqrt{1-\cos^2(\alpha)}$

Plugging the numbers, we have

$\sin(\alpha)=-\sqrt{1-\dfrac{64}{289}}=-\sqrt{\dfrac{225}{289}}=-\dfrac{15}{17}$

Now, just recall that

$\sin(-\alpha)=-\sin(\alpha)$

to deduce

$\sin(-\alpha)=-\sin(\alpha)=-\left(-\dfrac{15}{17}\right)=\dfrac{15}{17}$

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