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Old 04-28-2012   #1
xine
 
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Default The Cosine Curve

Hi there I would like to know how to do the following questions without drawing a graph. What is the formula?

The question: Express each of the following in terms of the cosine of another angle between 0 and 180

a) cos 20
b) cos 85


Thank you for any help!
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Old 04-29-2012   #2
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The title is misleading - you do not need to use a cosine curve. You need to look at the unit circle instead.



Here is a diagram, which shows you an example of how to use it. Say, you're looking for other answers for cos 30. The other answers would be the ones shown in the diagram, but for the "Sine" and "Tan" quadrant, it will be negative, for the "Cos" quadrant it will be positive. So:
cos 30 = -cos 150 = cos 210 = -cos 330.

Now, refering to your questions:

Cos 20 = -cos 170. You can check it up on a calculator to check.
Cos 85 = -cos 175.

I hope you understand the above stuff, I wasn't too clear!
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Old 04-30-2012   #3
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Quote:
Originally Posted by noreply View Post
The title is misleading - you do not need to use a cosine curve. You need to look at the unit circle instead.



Here is a diagram, which shows you an example of how to use it. Say, you're looking for other answers for cos 30. The other answers would be the ones shown in the diagram, but for the "Sine" and "Tan" quadrant, it will be negative, for the "Cos" quadrant it will be positive. So:
cos 30 = -cos 150 = cos 210 = -cos 330.

Now, refering to your questions:

Cos 20 = -cos 170. You can check it up on a calculator to check.
Cos 85 = -cos 175.

I hope you understand the above stuff, I wasn't too clear!
Actually cos 20 = -cos 160 and cos 85 = -cos 95

Think of the angles 20 and 85 being reference angles. In the case of the cosine function if the reference angle is between 0 and 90 degs, then the equivalent cosine for an angle between 90 and 180 degs is equal to:
-cos(180 - ref.)

So cos ref = -cos(180 - ref)

Or if you want to use a different angle (say one in Quadrant IV) then:

cos ref = cos(360 - ref) = cos (-ref)

Example: cos (30) = cos (330) = cos (-30)
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Old 05-01-2012   #4
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Yeah, that's correct. I wasn't refering to the diagram at the time, so I was slightly thinking on the spot.

Thanks for checking it for me!
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Old 05-21-2012   #5
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Also remember that cos(x) = cos(x+k*360) and cos(-x+k*360)
sine(x) = sine(180-x+2k*180) and sine(x+k*360)
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