SOLUTION: Determine the solutions to sin^2 θ = -sin θ where -π≤x<π

Algebra.Com
Question 1193294: Determine the solutions to sin^2 θ = -sin θ where -π≤x<π
Found 3 solutions by ikleyn, greenestamps, Solver92311:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
Determine the solutions to sin^2 θ = -sin θ where -π≤x<π
~~~~~~~~~~~~~ 

One solution is obvious: it is sin(θ) = 0,  which gives two answers  θ = 0  and 
θ = -,  belonging to the given interval.


To find another solution with sin(θ) =/= 0,  divide the original equation by sin(θ), both sides.


You will get then  sin(θ) = -1, which has the solution  θ = -  belonging to the given interval.


Thus there are three answers in the given interval:  θ = 0,  θ = -  and  θ = -.    ANSWER

Solved.



Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!




This is a quadratic equation with "sin(x)" as the "variable". Solve like any quadratic equation: get everything on one side set equal to 0 and factor.




sin(x)=0 OR sin(x)=-1

On the specified interval, sin(x)=0 at x=-pi and x=0; sinx=-1 at x=-pi/2.

ANSWERS: x=-pi, x=-pi/2, and x=0
Answer by Solver92311(821)   (Show Source): You can put this solution on YOUR website!

Since and are two entirely different things, is meaningless with respect to the given equation. Therefore you must need the solution for all real values of

[1]


[2]

Since ,
is a partial solution.

Furthermore, dividing eq. [2] by gives

[3]

Since ,
is also part of the solution set.

In sum, the solution set is

John

My calculator said it, I believe it, that settles it

From
I > Ø
RELATED QUESTIONS

Find all solutions to the equation. 7 sin^2(x) - 14 sin x + 2 =... (answered by lwsshak3)
Find all solutions to the equation. 7 sin^2 x - 14 sin x + 2 =... (answered by ikleyn,josmiceli)
Find all solutions to the equation. 7 sin^2 x - 14 sin x + 2 =... (answered by greenestamps)
Find all solutions to the equation. 7 sin^(2)x - 14 sin x + 2 =... (answered by KMST,Edwin McCravy)
7 sin^2 x - 14 sin x + 2 = -5 Find all solutions to the... (answered by ikleyn)
Please help!!!! State all the solutions to sin(x) + 2 sin(2x)=... (answered by Edwin McCravy)
What is the solution to the following equation: SIN^2(X) + SIN(x) = 2. Started from... (answered by scott8148)
Find all solutions to the equation in the interval (0,2pi).... (answered by KMST,tommyt3rd)
Find all solutions to the equation. 7 sin^2x - 14 sin x + 2 = -5 Show all your... (answered by Fombitz,MathTherapy)