Prepare an ALGEBRAIC solution to this problem Include EXACT

Prepare an ALGEBRAIC solution to this problem, Include EXACT ANSWERS in radian and degree form. Include approximate answers for the radian measures. Also include a computer-generated graphic model that confirms your algebraic results. You may choose to label the x-axis in degree or in radian mode. The points corresponding to solutions on [0, 2pi) must be marked. No other points are to be marked. The problem is 2sin^2(x)+7sin(x)=4 (that is 2sin squared). I need to know which quadrants they are in as well as the referance angle. Thanks for any and all help.

Solution

2sin^2(x)+7sin(x)=4

2sin^2(x)+7sin(x)- 4 =0

2sin^2(x) +8sinx -sinx -4 =0

2sinx(sinx +4) -1(sinx+4) =0

(2sinx -1)(sinx +4) =0

siin x+4 ---neglect as sinx cannot be less than -1

son 2sinx-1 =0 ----> sinx =1/2

As sin is +ve , son x cn be in Ist and IInd quadrants

So, x = sin^-1(1/2) , x= pi -sin^-1(1/2)

x =pi/6 = 0.52 rad, 30 deg

x = 2.62 , 150 deg

Solution : x= 0.52 , 2.62 radians

x= 30 , 150 deg