SOLUTION: Given: cscx=5/3; secx<0 Find exact values: a. cos (2x) b. tan (2x) c. sin (2x) I have tried using the pythagorean theorem: 3^2+b^2=5^2

Question 308497: Given: cscx=5/3; secx<0
Find exact values: a. cos (2x)
b. tan (2x)
c. sin (2x)
I have tried using the pythagorean theorem: 3^2+b^2=5^2
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Given: cscx=5/3; secx<0
-------------------------
csc = 1/sin
sin(x) = +3/5 --> Quad 1 or 2
-------------
sec<0 --> Quad 2 or 3
--> Quadrant 2
cos(x) = -4/5
-----------------
-----------------
Find exact values:
a. cos (2x)
= 1 - 2sin^2(x)
= 1 - 2*(3/5)^2 = 1- 18/25
= 7/25
------------
c. sin (2x)
= 2 sin(x) cos(x)
= 2(3/5)*(-4/5)
= -24/25
-----------
b. tan (2x) = sin(2x)/cos(2x)
= -24/7

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