Trigonometry Beyond Right Triangles · Strategy summary

Trigonometry Beyond Right Triangles: strategy summary

1. $180^\circ = \pi$ radians. Degrees to radians: multiply by $\frac{\pi}{180}$. Radians to degrees: multiply by $\frac{180}{\pi}$.
2. Arc length $s = r\theta$ with $\theta$ in radians. With degrees, convert first or use $\frac{\theta}{360} \cdot 2\pi r$.
3. On the unit circle the point at angle $\theta$ is $(\cos\theta, \sin\theta)$. Know the values at $30^\circ$, $45^\circ$, $60^\circ$, and $90^\circ$ from the 30-60-90 and 45-45-90 triangles.
4. Reference angle: measure to the x-axis. Signs: all positive in quadrant I; positive in II: sine; in III: tangent; in IV: cosine. Coterminal angles differ by $360^\circ$ or $2\pi$.
5. $\sin^2\theta + \cos^2\theta = 1$, $\tan\theta = \frac{\sin\theta}{\cos\theta}$, $\csc\theta = \frac{1}{\sin\theta}$, $\sec\theta = \frac{1}{\cos\theta}$, $\cot\theta = \frac{\cos\theta}{\sin\theta}$, and $\sin(90^\circ - \theta) = \cos\theta$.
6. Law of sines $\frac{a}{\sin A} = \frac{b}{\sin B}$ when you know an angle and the side across from it (AAS, ASA or SSA); law of cosines $c^2 = a^2 + b^2 - 2ab\cos C$ for SAS and SSS. Pair each side with the angle across from it.
7. For $y = a\sin(b(x - h)) + k$: amplitude $|a|$, period $\frac{2\pi}{b}$ (or $\frac{360^\circ}{b}$), midline $y = k$, maximum $k + |a|$, minimum $k - |a|$.
8. Before you use a calculator, check degree or radian mode.