Find all the solutions of the equation 3sin^2(x)-7sin(x)+2=0. The answers is x1=_______, x2=__________. x1

Question

Find all the solutions of the equation 3sin^2(x)-7sin(x)+2=0. The answers is x1=_______, x2=__________. x1<x2

campbell_st · Answer

this is basically a quadratic equation that can be factored 

any ideas..?

anonymous · Answer

(3sin(x)-1)(sin(x)-2)=0. Is that right?

campbell_st · Answer

thats correct... so you need to solve 

3sin(x) - 1 = 0   and  sin(x) - 2 = 0

so what solutions do you get....in the form  sin(x) =

anonymous · Answer

sin(x)=1/3 and 2

anonymous · Answer

@campbell_st

campbell_st · Answer

great... so what do you know about 

sin(x) = 2

anonymous · Answer

It's no solution right?

campbell_st · Answer

that's correct, it's undefined

so you only case is 

sin(x) = 1/3

so there are solutions in the 1st and 2nd quadrants

anonymous · Answer

I don't know how to find those solutions. @campbell_st

campbell_st · Answer

well I'd probably express it ad decimal radians 

find 

$$x = \sin^{-1}(\frac{1}{3})$$

so 1st quadrant angle is x

2nd quadrant angle is  180 - x