Graphing Trigonometric Functions

Graphing Trigonometric Functions

GCSE(H),

The values of sin(x), cos(x) and tan(x) are shown on a graph, below. Note that sin(x) and cos(x) repeat every 360º. Tan(x) repeats every 180º.

The range, in degrees, is normally given e.g. solve for 0º < x < 360º. Note that the value of the degree may be negative, or greater than 360º.

graph of sin/cos graph of tan

The graphs can be used to find the inverse function. To find the value of sin-1(0.5), find 0.5 on the y-axis, read across to the curve, then down to read 30º - or 390º, or even -210º.

circle showing sin/cos/tan values

The graphs can be derived by examining a circle of radius 1. The sin value for an angle can be obtained by reading from the vertical axis. The cos value can be obtained by reading from the horizontal axis. The tan value can be obtained by reading from a scale that is a tangent to the circle (in this case, the tangent is at x = 1).

Examples

1. Using a graph showing the cos function, determine the value of cos-1(0) when the angle is between 200 and 400 degrees.

Answer: 270º

Between 200º and 400º, the graph of the cos function passes through y = 0 when the angle is 270º.

2. Give one angle where sin(x) is negative, when 0 < x ≤ 360º.

Answer: Any angle from 180º to 360º.

Examine the graph of sin(x) to confirm.