Sine: starts at 0, peaks at 1 ($90°$), period $360°$. Cosine: starts at 1, dips to $-1$ ($180°$), period $360°$. Tangent: period $180°$, no amplitude, asymptotes at $90°, 270°,\ldots$

Reflex: Sine starts at the centre; cosine starts at the top; tangent repeats every $180°$ and has no top.

$$\begin{gathered}\sin, \cos: \ \text{Period} = \frac{360°}{b} \ \text{or} \ \frac{2\pi}{b}\\[3pt] \tan: \ \text{Period} = \frac{180°}{b} \ \text{or} \ \frac{\pi}{b}\end{gathered}$$

$b$ = how many basic graphs fit in $360°$ (or $180°$ for tan).

Reflex: Tangent's base period is half of sine's — don't reuse $\frac{360°}{b}$ for tan.

$$y = a\sin bx + c$$

a = amplitude (negative a reflects in x-axis), b = cycles per 360°, c shifts up/down. Centre line y=c; max c+|a|; min c−|a|. Reflex: Draw the centre line first, then the peaks.

$$y = -2\sin 2x$$

The negative reflects the curve in the $x$-axis — it starts by going DOWN. Amplitude is still 2; amplitude is a distance and never negative. Reflex: Negative $a$ changes the starting direction, not the size.

$$\begin{gathered}c = \frac{M + m}{2}\\[2pt] a = M - c\\[2pt] b = \frac{360° \text{ or } 2\pi}{\text{period}}\end{gathered}$$

Centre = mid of max/min; amplitude = peak minus centre; period gives $b$.

Reflex: Centre first, then amplitude, then period → b. Three reads, three constants.

$$\begin{gathered}2 + 4\cos 2x = 10 - \frac{3x}{\pi}\\[3pt] \Rightarrow\ \underbrace{1 + 2\cos 2x}_{f(x)} = 5 - \frac{3x}{2\pi}\end{gathered}$$

Rearrange (dividing through if needed) until one side matches your sketched $f(x)$ EXACTLY. Draw what's left as the line; count intersections.

Reflex: Massage the equation until one side IS your sketched function — whatever remains is the line to draw.