How do you solve #2sinxcosx + sinx = 0#?
1 Answer
Apr 14, 2015
To solve a trig equation, transform it to a few basic trig equations. Solving trig equations finally results in solving basic trig equations.
Reminder: 4 basic trig equations are: sin x = a; cos x = a; tan x = a; cot x = a.
f(x) = sin 2x + sin x = 2sin xcos x + sin x = 0.
f(x) = sin x(2cos x + 1 ) = 0.
Next, use the trig unit circle and trig table to solve the 2 basic trig equations: sin x = 0, and (2cos x + 1) = 0.
sin x = 0 --> x = 0; x = Pi; x = 2Pi (within interval 0 - 2Pi).
2cos x + 1 = 0 --> cos x = -1/2 --> x = 2Pi/3; x = 4Pi/3.
Answers inside period (0, 2Pi):
0; 2Pi/3; Pi; 4Pi/3; and 2Pi.
