Question 368413: What is the solution for the exact value of cos195 degrees?
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! Find the exact value of cos195 degrees.
The key is to write 195 degrees as the sum or difference of two numbers whose sine and cosine are known.
cos195 = cos(45 + 150).
NOTE: 45 + 150 = 195.
We need to use the sum formula for cosine.
We use this: cos(A + B) = cosAcosB - sinAsinB
Let A = 45 and B = 150
cos(45 + 150) = cos45cos150 - sin45sin150
If you memorized the unit circle (as you should to make your trig life easier), you will know the following:
cos45 = sqrt[2]/2
cos150 = -sqrt[3]/2
sin45 = sqrt[2]
sin150 = 1/2
cos(45 + 150) = sqrt[2]/2 * -sqrt[3]/2 - sqrt[2]/2 * 1/2
cos(45 + 150) = (-sqrt[6] - sqrt[2])/4
So, the exact value of cos195 degrees is (-sqrt[6] - sqrt[2])/4
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