Question

Connections Academy Sample Work Pre Calc

Please Help!!!
I believe
y (theta) = 3 sin t
and
a(theta) = 3 cos t
but that might be wrong because I'm so confused. Please Please help!

Answer 1

Explanation:

1. sintheta=y/3"

theta=sin-¹(y/3")

cos theta=a/3"

theta=cos-1(a/3)

sin beta=y/7"

beta=sin-¹(y/7")

b=√{y²+7" ²}

sorry last one I don't know

Answer 2

• sinθ = y/3 ⇒ y(θ) = 3 sinθ
• cosθ = a/3 ⇒ a(θ) = 3 cosθ
• sin β = y/7 = 3 sinθ / 7 ⇒ β(θ) = arcsin (3/7sinθ)
• b(θ) = √(7²-y²) = √(49-9sin²θ)
• p(θ) = a(θ) + b(θ) = 3 cosθ + √(49-9sin²θ)

The graph is attached

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p.s.

b(θ) can be put in different way:

• cos β = b/7 ⇒ b(θ) = 7 cos β = 7cos(arcsin(3/7sinθ))

Then

• p(θ) = a(θ) + b(θ) = 3 cosθ + 7cos(arcsin(3/7sinθ))

This doesn't change the function or the graph