Family Overview

In Plain Language

Topic 3.3 is about finding coordinates and exact sine/cosine values.

• On a circle of radius $r$ centered at the origin, the terminal ray meets the circle at $P=(r\cos\theta,\, r\sin\theta)$ (3.3.A.1).
• Exact values for multiples of $\pi/6$ and $\pi/4$ (terminal ray not on an axis) come from 45-45-90 and 30-60-90 geometry, with quadrant signs applied (3.3.A.2).

Why It Matters

These coordinates and exact values power Unit 3 graphs, models, and FRQ calculations. Knowing $(r\cos\theta, r\sin\theta)$ connects the unit-circle definitions from 3.2 to any radius.

How Families Can Help

• Practice the reference-angle chart: $\pi/6$, $\pi/4$, $\pi/3$ with positive QI values, then flip signs by quadrant.
• Ask: "What is $P$ if $r=2$ and $\theta=\pi/3$?"
• Drill axis angles too: $0$, $\pi/2$, $\pi$, $3\pi/2$.

What Not to Do

• Do not forget the factor $r$ when the circle is not unit.
• Do not drop the quadrant sign after finding the reference value.
• Do not mix up which special triangle goes with $\pi/6$ vs $\pi/4$.