<PRE><B>Question 368413</B>
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


mrfeliz.webs.com








</PRE>