AP Precalculus / Unit 3: Trigonometric and Polar Functions
3.10 Trigonometric Equations and Inequalities
Notes
Solve for the angle, then list all solutions using the period:
- $\displaystyle \sin x=\frac{1}{2}$: $\displaystyle x=\frac{\pi}{6}+2n\pi$ or $\displaystyle \frac{5\pi}{6}+2n\pi$.
- For inequalities, use the graph or unit circle to find intervals.
Practice
Solutions of $\cos x=0$ on $[0,2\pi)$:
Where the unit circle $x$-coordinate is 0.
Solutions of $2\sin x=1$ on $[0,2\pi)$:
Sine is positive in quadrants I and II.
$\tan x=1$ has general solution:
Tangent has period $\pi$.
Ready for more? Take the Unit 3 test.