# Trigonometry

posted by .

Solve sin 2x + sin x = 0 for 0 (Less then or equal to) x (Less then or equal to) 2pi.

• Trigonometry -

sin(2x)=2sin(x)cos(x)
so
sin(2x)+sin(x)=0
=>
2sin(x)cos(x)+sin(x)=0
sin(x)[2cos(x)+1]=0
sin(x)=0 or cos(x)=-1/2
sin(x)=0 => x=0, x=π for 0≤x<2π
cos(x)=-1/2 => x=2π/3 or x=4π/3

Combining, the solution set
S={0,2π/3,π 4π/3}
0≤x≤2π

## Similar Questions

1. ### math

Find intervals on which the following functions are increasing and decreasing. 1. f(x) = sin 2x : x is greater than or equal to 0 and less than or equal to pi 2. y = sin x + cos x [0,2pi]
2. ### i lied. very quick calc problem.

f(x) = abs(sin(x)), -pi less than or equal to x less than or equal to pi g(x) = x^2 let H(x) = g(f(x)) i got that H(x) would equal sin^2(x). THIS IS WHERE I AM STUCK! find the domain of H. do i still need to account for "-pi less than …
3. ### Trigonometry

4. Find the exact value for sin(x+y) if sinx=-4/5 and cos y = 15/17. Angles x and y are in the fourth quadrant. 5. Find the exact value for cos 165degrees using the half-angle identity. 1. Solve: 2 cos^2x - 3 cosx + 1 = 0 for 0 less …
4. ### Precalculs

I have no idea how to do these type of problems. -------Problem-------- Solve each equation on the interval 0 less than or equal to theta less than 2 pi 42. SQRT(3) sin theta + cos theta = 1 ---------------------- There is an example …
5. ### Math/Trig

Solve: sin x - 2sin x cos x = 0 for 0 is less than or equal to x is less than 2pi.
6. ### trigonometry

Solve the equation 6 cos x^2+sin x=4 if 0 is less than or equal to x is less than or equal to pi
7. ### Trigonometry

Thank you STEVE!!!!! Suppose that Cos (theta) = 1/square root 2 if 0<equal to theta , pi/2 then sin(theta) = tan (theta) = If 3pi/2 less than equal to theta , 2pi then sin(theta) = tan (theta) = I know the trig functions but I feel …
8. ### Trigonometry

Solve for the following equation to the nearest degree if needed for 0 less than equal to x less than equal to 360. sin^2x=cosx 2sin^2x+cosx-cos^2x=0
9. ### Pre Calc

Solve 2 sin^2 x-3 sin x+1 =0, 0 less than or equal to x < 2pi
10. ### math

cosxtanx-sin^2x=0 solve for x over the domain 0 is less than or equal to x which is less than or equal to 2pi

More Similar Questions