Trig graphs · Year 13
In Year 13 you get fluent with: transforming trig graphs.
The graphs of sin x and cos x are waves that repeat every 360°, staying between −1 and 1; the graph of tan x repeats every 180° and has vertical asymptotes. Changing the equation stretches or moves the graph in predictable ways.
Key facts
- y = sin x: starts at 0, maximum 1 at 90°, minimum −1 at 270°, period 360°.
- y = cos x: starts at 1, minimum −1 at 180°, period 360°.
- y = tan x: period 180°, asymptotes at 90°, 270°, …
- y = a sin x stretches vertically (max a); y = sin bx has period 360° ÷ b.
- y = sin x + d moves the graph up d; y = sin(x − c) moves it right c.
- Symmetry gives second solutions: sin x = k → x and 180° − x; cos x = k → x and 360° − x.
Worked examples
Example 1
Which equation is this graph: y = sin x, y = 2 sin x or y = sin 2x?
Answer: y = 2 sin x