Cos(-21/3pie)

[VVVCCCEEE]

Hey, could you guys tell me which one is right?

Find the exact vaule of cos (-21/3pie)?

1.
Cos(-7pie)
-cos(7pie)---> (6pie+ pie)
-cos(pie) --->(-1,0)
-1 (I'm not sure why the negatives don't cancel out)


2.
Cos(-7pie)--->(-6pie-pie)
cos(-pie)
-Cos(pie) --->(-1,0)
-1

[Opengangs]

Notice that \(\cos\) is even, so that tells us that: \(\cos(-x) = \cos x\).

So, we know that:
\[ \cos\left(-\frac{21\pi}{3}\right) = \cos\left(\frac{21\pi}{3}\right) \]

Reducing this, we get:
\[ \begin{align*}\cos\left(\frac{21\pi}{3}\right) &= \cos\left(7\pi\right) \\ &= \cos\left(6\pi + \pi\right) \\ &= \cos(\pi) \\ &= -1\end{align*}\]

Since \(6\pi\) is a multiple of \(2\pi\), then all we've really done is 3 full revolutions around the unit circle, and so it's equivalent to \(\cos(2\pi + x) \).

[VVVCCCEEE]

 Ohh right. Thankss, forgot that cos was even