Potcharapol S. answered • 11/03/24
Tutor
New to Wyzant
Remember that the inverse trigonometry is a function that returns an angle. The general approach is to assign an angle as the return value.
In this case, let θ = tan-1 (12/15). We want to evaluate sin 2θ.
Since tan θ = 12/15, we have sin θ = 12/√122+152 and cos θ = 15/√122+152 .
Therefore, sin 2θ = 2sinθcosθ = (2*12*15)/(122+152) = 40/41.
Alternatively, if you know the formula sin 2θ = 2tanθ / (1+tan2θ). Then you can simply plug the value and get sin 2θ = 2(12/15) / (1+(12/15)2) = 40/41.
Raymond B.
if you had just reduced 12/15 to 3/5 it would have simplified things plus make errors less likely
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20h
Raymond B.
have you checked this with a calculator? 15/17 seems to fit with what a calculator has, and not 40/41. but you get 3 up votes from students who apparently are happy with a false answer20h