AP Precalculus / Unit 3: Trigonometric and Polar Functions
3.2 Sine, Cosine, and Tangent
Notes
In a right triangle: $\displaystyle \sin\theta=\frac{\text{opp}}{\text{hyp}}$, $\displaystyle \cos\theta=\frac{\text{adj}}{\text{hyp}}$, $\displaystyle \tan\theta=\frac{\text{opp}}{\text{adj}}$.
- On the unit circle, a point at angle $\theta$ is $(\cos\theta,\sin\theta)$ and $\displaystyle \tan\theta=\frac{\sin\theta}{\cos\theta}$.
- Radians: $\pi$ radians $=180°$.
Practice
$\sin\theta$ for a right triangle with opposite 3 and hypotenuse 5:
Opposite over hypotenuse.
90° in radians:
$\displaystyle 90\cdot\frac{\pi}{180}$.
On the unit circle, the $x$-coordinate of the point at angle $\theta$ is:
$(\cos\theta,\sin\theta)$.
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