Trigonometric Equations

Summary

The general solution of sin x = k is	180°n + (-1)n sin-1 k      for all integer n
The general solution of cos x = k is	360°n ± cos-1 k      for all integer n
The general solution of tan x = k is	180°n + tan-1 k      for all integer n

Exercises for students
Find the general solution of the following equations and check your working using the above applet:

sin 2x = 0.5	sin (2x + 30°) = 0.5	cos 2x = 0.5
tan 2x = 0.5	sin x = sin 30°	cos x = cos 30°
tan x = tan 30°	sin 2x = sin 30°	cos 2x = cos 30°
sin 2x = sin 4x	cos 2x = cos 4x	tan 2x = tan 4x
sin 2x = cos 4x	cos 2x = sin 4x	tan 2x = cot 4x
3 sin x + 4 cos x = 5	3 sin x - 4 cos x = 5	3 sin 2x + 4 cos 2x = 5

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