SOLUTION: Can you please help me solve this equation: {{{ 4sin^2(x)+7sin(x)=2 }}} with the range of theta being between 0 and 2pi. I have gotten one answer, {{{ sin(x)=1/4 }}} or {{{ x=sin^-

Algebra ->  Trigonometry-basics -> SOLUTION: Can you please help me solve this equation: {{{ 4sin^2(x)+7sin(x)=2 }}} with the range of theta being between 0 and 2pi. I have gotten one answer, {{{ sin(x)=1/4 }}} or {{{ x=sin^-      Log On


   

Question 1076009: Can you please help me solve this equation: +4sin%5E2%28x%29%2B7sin%28x%29=2+ with the range of theta being between 0 and 2pi. I have gotten one answer, +sin%28x%29=1%2F4+ or +x=sin%5E-1%281%2F4%29+ , however it seems as though there's another one that I'm not able to find. Thank you!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution,
u=sin%28x%29
.
.
4u%5E2%2B7u-2=0
%28u%2B2%29%284u-1%29=0
Two "u" solutions:
u%2B2=0
u=-2
sin%28x%29=-2
No x solution here.
4u-1=0
4u=1
u=1%2F4
sin%28x%29=1%2F4
There are two solutions here:
x=14.5 and x=165.5