Family Overview

In Plain Language

Topic 3.2 defines sine, cosine, and tangent from the unit circle (and related circles centered at the origin).

• Standard position: vertex at the origin; initial ray along the positive $x$-axis; other ray is the terminal ray. Positive angles rotate counterclockwise; negative angles clockwise. Coterminal angles differ by full revolutions (3.2.A.1).
• Radians: arc length divided by radius; on the unit circle, radian measure equals arc length (3.2.A.2).
• Sine: vertical displacement of intersection point $P$ over distance $OP$; on the unit circle, $\sin\theta = y$ (3.2.A.3).
• Cosine: horizontal displacement over $OP$; on the unit circle, $\cos\theta = x$ (3.2.A.4).
• Tangent: slope of the terminal ray (when defined) $= y/x = \sin\theta/\cos\theta$ (3.2.A.5).

Why It Matters

This is the geometric foundation for all later Unit 3 trig work. AP items ask for coordinates, signs by quadrant, coterminal angles, and $\tan$ as slope.

How Families Can Help

• Draw the unit circle; mark $P=(x,y)$ and say "$x$ is cos, $y$ is sin."
• Practice "terminal ray slope = tan" when $x\neq 0$.
• Convert a simple degree measure to radians using $\pi$ radians $= 180^\circ$.

What Not to Do

• Do not memorize SOH-CAH-TOA as the only definition and ignore the circle.
• Do not forget $\tan$ is undefined when $\cos=0$ (vertical terminal ray).
• Do not mix up which coordinate is sine vs cosine.