Trigonometry · Quick Reference

Graphs Cheat Sheet

Trigonometry · Lesson 4/8

In one line: the graphs of sine, cosine, and tangent reveal their repeating wave-like nature — key properties like amplitude and period describe exactly how they repeat.

Key Ideas

1Periodic Functions. A function that repeats its values in regular intervals; sine and cosine repeat every 360° (2*pi radians).

2Amplitude. Half the distance between the maximum and minimum values of a wave; for y=A*sin(x), the amplitude is |A|.

3Period. 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).

4Key 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.

5Tangent's Graph. Unlike sine and cosine, tangent has a period of 180° (pi radians) and has vertical asymptotes where cosine equals 0.

Worked Examples

Find the amplitude of y = 3*sin(x).

Amplitude = 3

Find the period of y = sin(2x).

Period = 180°

Find the maximum and minimum values of y = 5*cos(x).

Max = 5, Min = -5

Formulas

Amplitude of A*sin(x) or A*cos(x) = |A|

Period of sin(Bx) or cos(Bx) = 360°/B (or 2*pi/B)

Practice Yourself

Find the amplitude of y=4*sin(x).

Find the period of y=cos(3x).

120°

Find the max value of y=2*sin(x).