SOLUTION: Given cos(t)=-3/4 with pi < t < {3pi}/{2}, find the values of the following trigonometric functions. Note: Give exact answers. cos(2t) = sin(2t) = cos(t/2)=

Question 930962: Given cos(t)=-3/4 with pi < t < {3pi}/{2}, find the values of the following trigonometric functions.
Note: Give exact answers.
cos(2t) =
sin(2t) =
cos(t/2)=
sin(t/2) =

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Given cos(t)=-3/4 with pi < t < {3pi}/{2}, find the values of the following trigonometric functions.
Note: Give exact answers.
cos(2t) =
sin(2t) =
cos(t/2)=
sin(t/2) =
***
reference angle t is in quadrant III where sin<0, cos<0
cost=-3/4
sint=-√(1-cos^2(t))=-√(1-9/16)=-√(7/16)=-√7/4
..
cos(2t)=1-2sin^2(t)=1-2(7/16)=1-14/16=2/16=1/8
sin(2t)=2sintcost=2*-(√7/4)*-(3/4)=6√7/16
cos(t/2)=-√((1+cost)/2)=-√((1-(3/4))/2)=-√(1/8)=-1/√8=-√8/8
sin(t/2)=√((1-cost)/2)=√((1+(3/4))/2)=√(7/8)
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