SOLUTION: if sin alpha = 1/ square root 5 , 0< alpha < pie by 2,. find the exact values of a) cos alpha b) sin2 alpha c) cos 2 alpha

Question 818904: if sin alpha = 1/ square root 5 , 0< alpha < pie by 2,. find the exact values of
a) cos alpha
b) sin2 alpha
c) cos 2 alpha
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Now we will use a square root of each side. Usually one needs to use a + when finding the square root of both sides of the equation. But since terminates in the 1st quadrant where all Trig functions are positive. So we only need the positive square root:

b)
Using sin(2x) = 2sin(x)cos(x) on this:

Now just substitute in (which was given) and which we found in part a. Then simplify.

c)
There are 3 variations to cos(2x). Any of them may be used. I'm going to use :

Now just substitute which we found in part a. Then simplify.
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