01 Key Concepts
Periodic Functions
A function that repeats its values in regular intervals; sine and cosine repeat every 360° (2*pi radians).
Amplitude
Half the distance between the maximum and minimum values of a wave; for y=A*sin(x), the amplitude is |A|.
Period
The length of one complete cycle before the graph starts repeating; for y=sin(Bx), the period is 360°/B (or 2*pi/B in radians).
Key Features of sin(x) and cos(x)
Both oscillate between -1 and 1. sin(x) starts at 0 and rises; cos(x) starts at 1.
Tangent's Graph
Unlike sine and cosine, tangent has a period of 180° (pi radians) and has vertical asymptotes where cosine equals 0.
02 Key Formulas
- Amplitude of A*sin(x) or A*cos(x) = |A|
- Period of sin(Bx) or cos(Bx) = 360°/B (or 2*pi/B)
03 Solved Examples
Example 1 Find the amplitude of y = 3*sin(x).
- The amplitude is the absolute value of the coefficient in front of sin.
- |3| = 3.
Answer: Amplitude = 3
Example 2 Find the period of y = sin(2x).
- Apply the formula: period = 360°/B, where B=2.
- 360/2.
Answer: Period = 180°
Example 3 Find the maximum and minimum values of y = 5*cos(x).
- Since cos(x) ranges from -1 to 1, multiplying by 5 scales this range.
- Max = 5*1 = 5. Min = 5*(-1) = -5.
Answer: Max = 5, Min = -5
04 Practice Questions
1Find the amplitude of y=4*sin(x).
4
2Find the period of y=cos(3x).
120°
3Find the max value of y=2*sin(x).
2
4What is the standard period of sin(x) with no coefficient?
360° (or 2*pi radians)
5What is the standard period of tan(x)?
180° (or pi radians)
📄 Graphs — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.