The cosine of anything is always a number between -1 and +1.
3 - (-7) = 10
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cos(5π//6) = -(√3)/2 ≈ -0.866
4/5
sin(t) = 2/3 sin2(t) + cos2(t) = 1 so cos(t) = ± sqrt[1 - sin2(t)] but because t is in the first quadrant, cos(t) > 0 so cos(t) = + sqrt[1 - sin2(t)] = sqrt[1 - 4/9] = sqrt[5/9] = sqrt(5)/3 Then sec(t) = 1/cos(t) = 1/sqrt(5)/3 = 3/sqrt(5) = 3*sqrt(5)/5
The integral of cos 5x is 1/5 sin (5x)
the height is 4.33 units cos 30 = .866 15 / 3 = 5 5 x .866 = 4.33