Find the exact value of the trigonometric function at the given real number.
1. cos (-13pi/20)

2. cos (10pi/3)

Question

Find the exact value of the trigonometric function at the given real number.
1. cos (-13pi/20)

2. cos (10pi/3)

e.mccormick · Answer

Just to confirm: (-13pi/20) or (-13pi/2) ?  I ask because the second is far simpler than the first.

e.mccormick · Answer

And with 2. cos (10pi/3)....

anonymous · Answer

i just need an explanation on how to solve the second one

e.mccormick · Answer

2. cos (10pi/3) ?

Do you know what coterminal angles are?

anonymous · Answer

isn't it the angle that's given is the terminal and the angle around is the other one?

e.mccormick · Answer

Well, on the unit circle there are many angles that represent the same thing.  The first of these you see is 0.  $0=2\pi$.  You can extend this and say: $0=2\pi = 4\pi = 6\pi$ and so on.

anonymous · Answer

so is 10pi/3 the same as another angle on the circle?

e.mccormick · Answer

Exactly!  The reason why this works is because the results of sine, cosine, tangent, and so on of those values are the same.

So, what is a coterminal of $\frac{10\pi}{3}$ that is between 0 and $2\pi$

e.mccormick · Answer

Subtract $2\pi$ from $\frac{10\pi}{3}$.  But be careful to make it into a fraction over 3 to do this!

anonymous · Answer

4pi/3? and why do you have to subtract 2pi from 10pi/3?

e.mccormick · Answer

It would be a full circle less, which is $2\pi$.  And yes, that makes $\frac{4\pi}{3}$ a cotermnal you could use.  Let me draw why.

e.mccormick · Answer

|dw:1370891885327:dw|You see how it adds a recolution?