SOLUTION: Given: cos (-105) Find the exact value of the function without the use of a calculator. I was unsure what to do with a negative, but from examples, I did the following where it

Algebra ->  Trigonometry-basics -> SOLUTION: Given: cos (-105) Find the exact value of the function without the use of a calculator. I was unsure what to do with a negative, but from examples, I did the following where it      Log On


   



Question 1114896: Given: cos (-105)
Find the exact value of the function without the use of a calculator.
I was unsure what to do with a negative, but from examples, I did the following where it "ignores" the negative.
cos (105) = cos (135 - 30)
+cos+%28135%29+cos+%2830%29+%2B+sin+%28135%29+sin+%2830%29+
+%28-sqrt%282%29%2F2%29%28sqrt%283%29%2F2%29+%2B+%28sqrt%282%29%2F2%29%281%2F2%29+
+%28-sqrt%286%29%2F4%29%2B+%28sqrt%282%29%2F4%29+
Final Answer: +%28sqrt%282%29-sqrt%286%29%29+%2F+%284%29+
If the final answer is right, why does the (-) go away and if that procedure is incorrect how would you split up the -105? Thank you for any help!

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
cos(a) = cos(-a) for any angle "a".



In particular,  cos(-105°) = cos(105°),  so your result is applicable to  cos(-105°).



Your final result is RIGHT:  cos(-105°) = %28sqrt%282%29-sqrt%286%29%29%2F4.