CPM Homework Help : APCALC Problem 11-7

Without a calculator, determine all values of $θ$ for which each of the polar curves cross the pole (origin). Then, graph the polar curve on your calculator and verify your answers.

$r=\ \sin(3θ)+\ \cos(3θ)$
Hint:
A polar curve intersects the origin when $r = 0$ .
Step 1(a):
$-\sin(3\theta)=\cos(3\theta)$
Step 2(a):
$\tan(3\theta)=-1$

$r=3\sin2(θ)-2$

Compute without a calculator