SOLUTION: 6cos^2(x)+3sin(x)=3 for (0 < x < 360) I've got to solution: sin(x)-1=0 x=90 Or 2sin(x)+3=0 sin(x)=-3/2 The second solution confuses me because I can't take arc sin -3/2

Algebra ->  Trigonometry-basics -> SOLUTION: 6cos^2(x)+3sin(x)=3 for (0 < x < 360) I've got to solution: sin(x)-1=0 x=90 Or 2sin(x)+3=0 sin(x)=-3/2 The second solution confuses me because I can't take arc sin -3/2      Log On


   

Question 1011622: 6cos^2(x)+3sin(x)=3
for (0 < x < 360)
I've got to solution:
sin(x)-1=0
x=90
Or
2sin(x)+3=0
sin(x)=-3/2
The second solution confuses me because I can't take arc sin -3/2. I must have made a mistake somewhere. Any help please?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52915) About Me  (Show Source):
You can put this solution on YOUR website!
.
6cos%5E2%28x%29%2B3sin%28x%29 = 3

2%2Acos%5E2%28x%29+%2B+sin%28x%29 = 1,

2%2A%281-sin%5E2%28x%29%29+%2B+sin%28x%29+-+1 = 0,

2%2Asin%5E2%28x%29+-+sin%28x%29+-+1 = 0.

Now introduce new variable y = sin(x) for brevity. The last equation takes the form

2y%5E2+-+y+-+1 = 0.

Solve this quadratic equation using quadratic formula. You will get 

y%5B1%5D = 1, y%5B2%5D = -1%2F2.

Now you need to solve two equations for x The first one is 

sin(x) = 1   -----> x = pi%2F2 + 2k%2Api, k = 0, +/-1, +/-2, . . . 

The second equation is 

sin(x) = -1%2F2. Its solutions are x = -pi%2F6 + 2k%2Api, k = 0, +/-1, +/-2, . . . 

Answer. Regarding the given interval for x, there are two solutions: x = pi%2F2 and x = 5pi%2F6.


Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

6cos^2(x)+3sin(x)=3
for (0 < x < 360)
I've got to solution:
sin(x)-1=0
x=90
Or
2sin(x)+3=0
sin(x)=-3/2
The second solution confuses me because I can't take arc sin -3/2. I must have made a mistake somewhere. Any help please?
Solve 2+cos%5E2+%28x%29+-+sin+x+-+1+=+0 ---------> (2 sin x + 1)(sin x - 1) = 0, to get:

highlight_green%28system%28matrix%281%2C3%2Csin+%28x%29+=+-+1%2F2%2C+or%2C+210%5Eo%29%29%29 (3rd quadrant)

highlight_green%28system%28matrix%281%2C3%2Csin+%28x%29+=+-+1%2F2%2C+or%2C+330%5Eo%29%29%29 (4th quadrant)

highlight_green%28system%28matrix%281%2C3%2Csin+%28x%29+=+1%2C+or%2C+90%5Eo%29%29%29 (Positive side of y-axis)