Year 10: Sketching trigonometric functions

Trigonometric graphs show how sine, cosine, and tangent values change as the angle changes. In Year 10, the main goal is to recognise the basic shape, key points, and repeating pattern.

Sine and cosine repeat every

360 °

. Tangent also repeats, but its graph has breaks where the function is undefined.

The sine graph

The sine graph starts at $(0 °, 0)$ , rises to $1$ at $90 °$ , returns to $0$ at $180 °$ , falls to $- 1$ at $270 °$ , and comes back to $0$ at $360 °$ .

Example 1: Sketch

y = \sin x

from

0 °

360 °

. Plot the five key points:

(0, 0)

(90, 1)

(180, 0)

(270, - 1)

(360, 0)

, then draw a smooth curve through them.

The cosine graph

Cosine begins at $1$ when $x = 0 °$ . That is the main visual difference from the sine graph.

Example 2: Key points for

y = \cos x

are

(0, 1)

(90, 0)

(180, - 1)

(270, 0)

(360, 1)

The tangent graph

Tangent passes through $(0 °, 0)$ and $(180 °, 0)$ , but it is undefined at $90 °$ and $270 °$ . Those become vertical asymptote lines on the sketch.

Example 3: When sketching

y = \tan x

, first mark

x = 90 °

and

x = 270 °

as undefined, then draw each branch rising through the intercepts.

Common mistakes

Plotting the right points but joining them with straight lines instead of smooth curves.
Forgetting that cosine starts at $1$ , not $0$ .
Drawing tangent through its undefined points.

Skills to practise

Sketch trigonometric functions