Expert: Scott A Wilson - 11/4/2009

Question
For y=3f(2pheta-90')-1   , f(pheta)=sin pheta
Evaluate for 30'

Answer
Is that y = 3f(2Θ-90°)-1?  By the way, Θ is alt-233 (numbers on the right) and ° is alt-248.
Also, ² is alt-253 and √ is alt-251.  In fact, A is alt-065, but it is easier to type A.

It looks like you mean y = sin(2Θ-90°)-1.

If you go over to -90° on the sin wave, the sin(-90°) is similar to -cos(0°).
In this way, we can say that sin(2Θ-90°) = -cos(2Θ).

Now cos(2Θ) = 2•cos²(Θ) - 1, so -cos(2Θ) = 1 - 2•cos²(Θ).

What this comes down to is y = 3•sin(2Θ-90°)-1 = -3•cos(2Θ) - 1 = -3(1 - 2•cos²(Θ)) - 1.

Multiplying it out gives -4 + 6•cos²(Θ).

Now to evaluate it at 30°, the cos(30°) = √3/2, so we have -4 + 6(√3/2)².
That is the same as -4 + 6(3/4) = -4 + 18/4 = -8/2 + 9/2 = 1/2.