Solving Equations Using the Unit Circle

[kylepetten]

Homework Statement

Find all solutions to the equation below such that -180° [tex]\leq[/tex] x [tex]\leq[/tex] 90°

2sin²x + sinx = 0

Homework Equations

The Attempt at a Solution

2sin²x + sinx = 0

sinx[2sinx + 1] = 0

sin x = 0 sinx= -1/2

x = {0° + 360°n
{-180° + 360°n
n[tex]\epsilon[/tex]I

 

[Mark44]

Homework Statement

Find all solutions to the equation below such that -180° [tex]\leq[/tex] x [tex]\leq[/tex] 90°

2sin²x + sinx = 0

Homework Equations

The Attempt at a Solution

2sin²x + sinx = 0

sinx[2sinx + 1] = 0

sin x = 0 sinx= -1/2

x = {0° + 360°n
{-180° + 360°n
n[tex]\epsilon[/tex]I

x = n*pi are the solutions to sin(x) = 0. What about the solutions to sin(x) = -1/2?

 

[kylepetten]

x = n*pi are the solutions to sin(x) = 0. What about the solutions to sin(x) = -1/2?

im not using equations, i am getting my exact values from the unit circle

 

[The Chaz]

im not using equations, i am getting my exact values from the unit circle

Yeah, Mark44!

 

[Mark44]

im not using equations, i am getting my exact values from the unit circle

You are using equations, namely 2sin²x + sinx = 0, which you rewrote as sinx(2sinx + 1) = 0.

You have found the solutions to the equation sinx = 0, but you haven't found any for the equation 2sinx + 1 = 0.

BTW, according to your problem description, you need be concerned only with values for which -180° <= x <= 90°. On this interval there are only two solutions to sinx = 0.

 

[willem2]

im not using equations, i am getting my exact values from the unit circle

If you post an equation here, it looks like you're using it.
sin x = 1/2 is another possibility. I'm certain that value of x is on the unit circle as well.
you didn't use the condition that -180<=x<=90. An answer such as 360n isn't acceptable here.

 

[Mark44]

If you post an equation here, it looks like you're using it.
sin x = 1/2 is another possibility. I'm certain that value of x is on the unit circle as well.
you didn't use the condition that -180<=x<=90. An answer such as 360n isn't acceptable here.

Probably a typo, but sin x = 1/2 is not a solution. sin x = -1/2 is a solution, though.