anonymous
  • anonymous
Find the exact value of the trigonometric function at the given real number. 1. cos (-13pi/20) 2. cos (10pi/3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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e.mccormick
  • e.mccormick
Just to confirm: (-13pi/20) or (-13pi/2) ? I ask because the second is far simpler than the first.
e.mccormick
  • e.mccormick
And with 2. cos (10pi/3)....
anonymous
  • anonymous
i just need an explanation on how to solve the second one

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e.mccormick
  • e.mccormick
2. cos (10pi/3) ? Do you know what coterminal angles are?
anonymous
  • anonymous
isn't it the angle that's given is the terminal and the angle around is the other one?
e.mccormick
  • e.mccormick
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
  • anonymous
so is 10pi/3 the same as another angle on the circle?
e.mccormick
  • e.mccormick
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
  • e.mccormick
Subtract \(2\pi\) from \(\frac{10\pi}{3}\). But be careful to make it into a fraction over 3 to do this!
anonymous
  • anonymous
4pi/3? and why do you have to subtract 2pi from 10pi/3?
e.mccormick
  • e.mccormick
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
  • e.mccormick
|dw:1370891885327:dw|You see how it adds a recolution?
e.mccormick
  • e.mccormick
revolution...
anonymous
  • anonymous
ohh so adding that 2pi to 4pi/3 gives you that 10pi/3?
anonymous
  • anonymous
and so because their the same..that makes them coterminal?
anonymous
  • anonymous
they're*..
e.mccormick
  • e.mccormick
Yes. And the coterminal is why you subtract 2pi from the 10pi/3 to get back to 4pi/3. And then 4pi/3 is something you know from your unit circle. That gievs you the exact value.
anonymous
  • anonymous
ok, and would it be the same for all of the other trig functions if the angle that's given, is in radians?
e.mccormick
  • e.mccormick
Well, if it is in degrees, you just ad or subtract 360 degrees as needed. So same principal. As long as you get a coterminal angle, you have the same value. So cos(4pi/3) is the same as cos(58pi/3).
e.mccormick
  • e.mccormick
And yes, this is true for all the trig funcions.
anonymous
  • anonymous
alright cool, thanks so much! that helped alot!
e.mccormick
  • e.mccormick
np. Have fun!

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