🌊 Trig Waves Quiz — Sine & Cosine Adventures!

📚 Core Concept: Amplitude & the Cosine Function

The parent function is $y = cos(θ)$ . When we multiply it by a number, we change its amplitude.

y = A · cos(θ)
Amplitude = |A| | Period = 2π | Domain = all reals | Range = [−|A|, |A|]

Step 1: Identify A = 3 → Amplitude = 3

Step 2: Table of key values (one full period 0 to 2π):

θ	0	π/2	π	3π/2	2π
cos(θ)	1	0	−1	0	1
3cos(θ)	3	0	−3	0	3

Step 3: Range = [−3, 3] | Domain = all real numbers

Amplitude = 4 | Period = 2π | Range = [−4, 4]

Key points: sin starts at 0, peaks at π/2 → 4, back to 0 at π, dips to −4 at 3π/2, returns to 0 at 2π.