| |
You are here: Experts > Science > Math for Kids > Word Problems > Transformations
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.
Add to this Answer Ask a Question
|
|
