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Vlad [161]
3 years ago
9

Let u = <-7, -2>. Find 8u.

Mathematics
1 answer:
Evgen [1.6K]3 years ago
8 0
<8 * (-7), 8 * (-2)>

<-56, -16>

Hope it helps, good work!
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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

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

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