Prepare an ALGEBRAIC solution to this problem, Include EXACT ANSWERS in radian a

Question

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.

Explanation / Answer

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

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