Graphs of sine and cosine, period and amplitude
Read the graphs of sine and cosine: where cosine is zero, how the period and the greatest value change in y = sin 2x and y = 2sinx + 1, and how secant and inverse sine are read from the same curves.
- UK: Year 10
- France: grade 11
- Germany: grade 10
- Iran: grade 11
- Afghanistan: grade 10
- Palestine: grade 9
- Ukraine: grade 10
- Russia: grade 10
Guide
For Afghan Grade 10 (chapter 4: graphs of trigonometric functions), Iran Grade 11–12 and GCSE/A-level. The x-axis counts in degrees (one square is 90°); the y-axis counts in halves or in ones.
y = sin x and y = cos x are waves between −1 and 1 that repeat every 360°; the cosine graph is the sine graph moved 90° to the left. The sine is zero at 0°, 180° and 360°; the cosine is zero at 90° and 270°.
In y = asinbx + c the number a is the amplitude (the height of a wave above the midline), the period is 360°b, and c moves the whole graph up. So the greatest value is a + c.
The reciprocal functions are secx = 1cos x, cscx = 1sin x and cot x = 1tan x. The inverse functions sin−1 and cos−1 are different: they turn a ratio back into an angle, and sin−1x is not 1sin x.