How to Find Period of a Graph?

Identify a repeating pattern in the graph

Find two consecutive points where the graph has the same position and direction

Measure the horizontal distance between those matching points

The horizontal distance is the period

For sine and cosine graphs, use the distance between repeating peaks, troughs, or matching midline crossings

For tangent and cotangent graphs, use the distance between repeating vertical asymptotes or matching branches

For transformed graphs, use the coefficient of x inside the function to adjust the basic period

Use the formula period = 2π / |b| for sine and cosine functions of the form y = a sin(bx + c) + d or y = a cos(bx + c) + d

Use the formula period = π / |b| for tangent and cotangent functions of the form y = a tan(bx + c) + d or y = a cot(bx + c) + d

Verify the pattern repeats exactly over the measured interval