The trigonometric functions $\sin$, $\cos$, and $\tan$ are defined for all angles, not just those in right-angled triangles.
Graphs:
$y = \sin x$: wave shape, period $360°$, range $[-1, 1]$, passes through $(0, 0)$ $y = \cos x$: wave shape, period $360°$, range $[-1, 1]$, passes through $(0, 1)$ $y = \tan x$: period $180°$, asymptotes at $x = 90°, 270°, \ldots$, no maximum or minimum
Key symmetry properties: $$\sin(180° - x) = \sin x$$ $$\cos(360° - x) = \cos x$$ $$\sin(-x) = -\sin x \quad (\sin \text{ is odd})$$ $$\cos(-x) = \cos x \quad (\cos \text{ is even})$$
CAST diagram — shows which functions are positive in each quadrant:
- All positive (0°–90°)
- Sine positive (90°–180°)
- Tangent positive (180°–270°)
- Cosine positive (270°–360°)
Used to find all solutions of trig equations in a given range.
Common error: only giving one solution to a trig equation — always check all quadrants in the given range.