SOLUTION: if sin x=4/5, where x is greater than 0 but less than 90 evaluate each of the following a) sin 2x b) cos 2x c) tan 2x

Algebra ->  Trigonometry-basics -> SOLUTION: if sin x=4/5, where x is greater than 0 but less than 90 evaluate each of the following a) sin 2x b) cos 2x c) tan 2x       Log On


   

Question 440916: if sin x=4/5, where x is greater than 0 but less than 90 evaluate each of the following
a) sin 2x
b) cos 2x
c) tan 2x
Answer by lwsshak3(11628) About Me  (Show Source):
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if sin x=4/5, where x is greater than 0 but less than 90 evaluate each of the following
a) sin 2x
b) cos 2x
c) tan 2x
..
If sin x=4/5, we are working with a 3-4-5 right triangle in quadrant I
Then, cos x=3/5
tan x=4/3
..
a) sin 2x=2sin x cos x=2*4/5*3/5=24/25
b) cos 2x=cos^2x -sin^2x=(3/5)^2-(4/5)^2=9/25-16/25=-7/25
c) tan 2x=2tanx/1-tan^2x=2*(4/3)/1-(4/3)^2
=(8/3)/1-16/9
=(8/3)/-7/9=-72/21
..
ans:
a) sin 2x=24/25
b) cos 2x=-7/25
c) tan 2x=-72/21