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 ٢x and y = ٢sin x + ١, and how secant and inverse sine are read from the same curves.
- فلسطين: الصف ٩
- إيران: الصف ١١
- أفغانستان: الصف ١٠
- أوكرانيا: الصف ١٠
- روسيا: الصف ١٠
- ألمانيا: الصف ١٠
- فرنسا: الصف ١١
- بريطانيا: السنة ١٠
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الدليل
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 جيب is zero at 0°, 180° and 360°; the تجيب 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 ٣٦٠°b, and c moves the whole graph up. So the greatest value is a + c.
The reciprocal functions are secx = ١cos x, cscx = ١sin x and cot x = ١tan x. The inverse functions sin−١ and cos−١ are different: they turn a ratio back into an angle, and sin−١x is not ١sin x.