SOLUTION: 3sin^2 theta -5sin theta +2 = 0

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Question 969313: 3sin^2 theta -5sin theta +2 = 0
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
3sin%5E2%28theta%29-5sin%28theta%29%2B2}%22%22=%22%22%220%22

matrix%281%2C2%2C+Use%2C+u-substitution%29

matrix%281%2C4%2CLet%2Csin%28theta%29%2C%22%22=%22%22%2Cu%29

matrix%281%2C4%2CThen%2Csin%5E2%28theta%29%2C%22%22=%22%22%2Cu%5E2%29

3u%5E2-5u%2B2%22%22=%22%22%220%22

%283u-1%29%28u-2%29%22%22=%22%22%220%22

3u-1=0,  u-2=0
3u=1,      u=2
u=1%2F3

matrix%281%2C5%2C++Now%2C+substitute%2C+sin%28theta%29%2C+for%2C+u%29
 
sin%28theta%29=1%2F3,   cross%28sin%28theta%29=2%29

We discard the second answer since the sine can only be
between -1 and +1.

Use the inverse sine function to get the value for q.

I'll let you finish, since you did not specify whether you want
degrees or radians, or whether you only want answers between 0° 
and 360°, or between 0 an 2p or whether you wanted a general 
solution in terms of an arbitrary integer n.

Edwin

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

3sin^2 theta -5sin theta +2 = 0
highlight_green%28sin%28theta%29+=+2%2F3%29%29, or highlight_green%28sin%28theta%29+=+1%29