sin(78*2.5) = sin(195) = -.2588
So, what's wrong?
sin 210 = -1/2
5/2 θ = 210,330,...
θ = 84,132,...
when you divided by 5/2, you also need to adjust the amount you add. It's best to get a positive reference angle and then work from there.
Solve the equation sin (5/2θ) = -1/2 for 0°≤0 ≤ 180°
sin(5/2θ) = -1/2
5θ/2 = -30
θ = -12
78, 168
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