Solve 2 sin x+ 3 cos x=0?

Question

Solve 2 sin x+ 3 cos x=0?

Answer 1

2sinx=-3cosx   sinx/cosx=-3/2   tanx=-1.5  x=taninverse-1.5

   x=-56.31

Answer 2

I love tangent I actually love trig more than I do geometry but can't help you with this one that was like wat 2 years ago for me and prob not even that

Answer 3

2 sin x + 3 cos x = k cos ( x - α ) for k > 0

2 sin x + 3 cos x = ( k cos α) cos x + (k sin α) sin x

2 = k sin α

3 = k cos α--------α in 1st quadrant

tan α = 2/3

α = 0.369 radians

4 + 9 = k ² ( sin ² α + cos ² α )

13 = k ²

k = √13

√13 cos (x - 0.369) = 0

x - 0.369 = π/2 , 3π / 2

x = 1.94 , x = 5.08 (for 0 ≤ x ≤ 2π)

Answer 4

Dont forget all of the other solutions:

2sin(x) + 3cos(x) = 0

2sin(x) = -3cos(x)

sin(x)/cos(x) = -3/2

tan(x) = -3/2

x = arctan(-3/2)

Now tan is negative in the 2nd and 4th quadrants so there are answers there

x = -56.3deg (1dp) is the solution in the fourth quadrant

so x = 180n - 56.3 is ALL solutions  

Answer 5

2 sin x+ 3 cos x=0

2sinx=-3cosx

2(sinx/cosx)=-3

tanx=-3/2

x=(invtan(3/2))