cosine is adjacent/hypotenuse
Need to find the third side of the triangle (opposite side) using pythagorean theorem which turns out to be 8
so sin(u) =8/17 and tan(u) =-8/15
now use your double angle formulas
sin(2u) = 2sin(u)cos(u)= (2)(8/17)(-15/17) =-240/289
cos(2u)=cos^2(u)-sin^2(u)= (-15/17)^2-(8/17)^2=
161/289
I will leave tan(2u) calculation to you
Stephen K.
tutor
The easiest and simplistic way to do this( my preferred method for doing any math problem) is to realize that tan(2u) = sin(2u)/cos(2u) These are values that we already have so tan(2u)= (-240/289)/(161/289) = -240/161
That was easy and helps you avoid the calculation errors you made. Lets look at what you did
Looking at the numerator (2)(-8/15) = -16/15 not -16/30
In the denominator 1-(-8/15)^2 = 1-64/225 not 1+64/225 (a negative squared is positive) which in fraction form is 161/225
(-16/15)/(161/225) will give you -240/161
Now you have to admit that the first method was a lot easier than yours
Hope this helps
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11/08/20
Uriel G.
Yes! thank you so much!
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11/08/20
Uriel G.
tan2u= 2tanu/1-tan^2u = 2(-8/15)/1-(-8/15)^2 = (-16/30)/1+(64/225) = = (-16/30)/(225/225)+(64/225) = (-16/30)/(289/225)= then you get rid of the denominator so you get (-16/30)(225/289) = so the answer is 3600/8670= which reduces to 120/289 ??11/08/20