SOLUTION: Please help me solve this question. Solve each of the following for 0 <= theta <= 360 degrees 3sin^2 theta + 2sin theta = 0

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me solve this question. Solve each of the following for 0 <= theta <= 360 degrees 3sin^2 theta + 2sin theta = 0      Log On


   

Question 1180791: Please help me solve this question.
Solve each of the following for 0 <= theta <= 360 degrees
3sin^2 theta + 2sin theta = 0
Found 3 solutions by MathLover1, Theo, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solve each of the following for 0+%3C=+theta+%3C=+360+°
3sin%5E2+%28theta%29+%2B+2sin%28+theta%29+=+0
%283sin%28theta%29+%2B+2%29sin%28+theta%29+=+0
solutions:
if %283sin%28theta%29+%2B+2%29+=+0=>3sin%28theta%29=-+2=>sin%28theta%29=-+2%2F3
sin%5E-1%28-2%2F3%29=-0.72972
since given 0+%3C=+theta+%3C=+360+°
theta=180%2Bsin%5E-1%28-+2%2F3%29°
theta=360-sin%5E-1%28-+2%2F3%29°
then
theta=180-0.72972
theta=180-41.81°
theta=138.19°
theta=360-%28-41.81%29°
theta=360%2B41.81°
theta=41.81°
if sin%28theta%29+=+0
theta=sin%5E-1%280%29
theta=0°
theta=0%2B180°
theta=180°
theta=0%2B360°
theta=360°
combine solutions:
sin%28theta%29+=+0
theta=41.81°
theta=138.19°
theta=180°
theta=360°


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
equation is 3sin^2(theta) + 2sin(theta) = 0
factor out sin(theta) to get:
sin(theta) * (3sin(theta) + 2) = 0
this is true when sin(theta) = 0 or 3sin(theta) + 2 = 0
solve for sin(theta) to get:
sin(theta) = 0 or sin(theta) = -2/3.
the reference angle (equivalent angle in the first quadrant) will be:
theta = arcsin(0) = 0 degrees.
theta = arcsin(2/3) = 41.8103149 degrees.
note that the trig function is always positive in the first quadrant.
sin(theta) is 0 when theta = 0 or 180 degrees or 360 degrees.
sin(theta) is negative in the third and fourth quadrants.
the reference angle of 41.8103149 in the third and fourth quadrant is found as follows:
third quadrant = 41.8103149 + 180 = 221.8103149 degrees.
fourth quadrant = 360 - 41.8103149 = 318.1896851 degrees.
your angles that satisfy the equation of 3sin^2(theta) + 2sin(theta) = 0 are:
0,180,360 degrees.
221.8103149, 318.1896851 degrees.
a graph of the equation is shown below:



Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.


Comparing the solutions by  @Theo and  @MathLover1,  notice that the solution by  @Theo is correct.

The solution by  @MathLover1 is   W R O N G,   showing lack of knowledge on elementary trigonometric functions.