From basics to graphing โ master trig functions step by step โจ
The parent function is y = cos(ฮธ). When we multiply it by a number, we change its amplitude.
Step 1: Identify A = 3 โ Amplitude = 3
Step 2: Table of key values (one full period 0 to 2ฯ):
| ฮธ | 0 | ฯ/2 | ฯ | 3ฯ/2 | 2ฯ |
|---|---|---|---|---|---|
| cos(ฮธ) | 1 | 0 | โ1 | 0 | 1 |
| 3cos(ฮธ) | 3 | 0 | โ3 | 0 | 3 |
Step 3: Range = [โ3, 3] | Domain = all real numbers
Amplitude = 4 | Period = 2ฯ | Range = [โ4, 4]
Key points: sin starts at 0, peaks at ฯ/2 โ 4, back to 0 at ฯ, dips to โ4 at 3ฯ/2, returns to 0 at 2ฯ.