SOLUTION: Find the exact values for sin2a, cos2a and tan2a given sin a= 1/2 and 0<a<pi/2. Thanks!!!

Question 838594: Find the exact values for sin2a, cos2a and tan2a given sin a= 1/2 and 0 Thanks!!!
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
We will use the equivalent expressions sin(2x) = 2 sin x cos x
Since sin(a) = 1/2 and sin(a) = (opposite side)/hypotenuse
To find the relative length of the third leg

opp = 1 , adj = sqrt(3) , hyp = 2
Since cos(x) = adj/hyp ,
cos(a) = sqrt(3)/2
Substituting sqrt(3)/2 for cos(a) and 1/2 for sin(a) in 2sin(a)*cos(a)
2*(1/2)(sqrt(3)/2) = (sqrt(3)/2)
Now we have
sin(2a)=
-------------
cos(2a) = cos^2(a) - sin^2(a)
cos(2a) =
cos(2a) =
cos(2a) =
cos(2a) =
-------------
tan(2a) = sin(2a)/cos(2a)
=
=
Summarizing
sin(2a)= ,cos(2a) = ,tan(2a) =
You may have noticed that for sin(a) = 1/2 a is 30 degrees
sin(60)= ,cos(60) = ,tan(60) =

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