Points, Vectors, and Functions Exercises

Answer

Since the function uses sin(3θ), it's a reasonable guess that values of θ in the family will be useful.

See what we find for .

That's a full petal, but not the one we want.

Try .

That's the part we want. The bounds for θ are .

Answer

Start with 0 ≤ θ ≤ π, since that seems to work a lot:

That's not enough graph. Try expanding the bounds for θ.

How about 0 ≤ θ ≤ 2π?

That's the right piece of the graph. The bounds we want are 0 ≤ θ ≤ 2π.

Answer

Try 0 ≤ θ ≤ π:

 No, that's too much graph. Since there's a in the argument to cosine.

Try knocking the upper bound down to .

That's not enough graph.

Try doubling the upper bound of θ, we have :

That's what we want. The final answer is .