Need help on solving Trig equations

[ConfusedMath]

Hello,

I am taking a precalc class and am having trouble when it comes to solving trig equations. Our book does not do a very good job on explaining and I have been unable to find any examples or similar problems to the following:

find all solutions ofin the interval [0,2pie) x representing theta.

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



cos(x)+sin(x)=0



cos(x/2)-1=2



2sin^2(x)=sin(x)



cos(2x)=sin(x)



cos(2x)=squareerootof 2 -cos(2x)



If anyone could explain the steps and how to solve these it would be greatly appreciated.

 

[Mrspi]

Hello,

I am taking a precalc class and am having trouble when it comes to solving trig equations. Our book does not do a very good job on explaining and I have been unable to find any examples or similar problems to the following:

find all solutions ofin the interval [0,2pie) x representing theta.

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

Well gee...this looks like a WHOLE assignment. Did you read the "rules for posting"?

We don't DO homework here, and we expect that you'll show us what you've done to attempt a problem. Giving us a whole list of questions, and asking for the steps to solve is a bit much, I think.

That said, I'll try to give you some hints on the FIRST problem.

You've got

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

Does that look like anything familiar?

HINT: You should have this "angle sum identity" in your book:

sin (A + B) = sin A cos B + cos A sin B

Compare this to your problem:

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

Using the identity I stated above, you should be able to resolve your equation to

sin (x + 3x) = 0

Or,

sin (4x) = 0


Where is the sine of an angle equal to 0? Use the unit circle.

sin (4x) = 0 when 4x = 0, or sin (4x) = 0 when 4x = pi

If 4x = 0, then x = 0. If 4x = pi, then x = pi/4

 

[mmm4444bot]

2sin^2(x)=sin(x)

If anyone could explain the steps and how to solve these it would be greatly appreciated.

1) Subtract sin(x) from both sides

2) Factor sin(x) out of the lefthand side

3) Use the Zero-Product Property, and set each factor equal to zero

4) Solve the two resulting equations for x

If you do not know how to solve sin(x) = 0 and sin(x) = 1/2, for values of x from zero up to (but not including) 2*Pi, then I'm thinking that you've probably fallen too far behind in your class for me to help you, over the Internet.

You stated that your book does not do a very good job of explaining. Tell us specifically what confuses you, in those examples, and we will explain it in greater detail, for you.

 

[ConfusedMath]

Thank you both.

No, this was not a whole assignment, the whole assignment had about 13 or more total but these were the ones I was stuck on. I'm not one of those people who post wanting people online to do their homework.

Yes I know how to find sin(x)=1/2&0
it's just the steps to getting there that I get stuck on. Our book tends toskip alot of steps and jump to answers without showing how they got to the answer.

 

[mmm4444bot]

Okay, but the set-ups are mostly algebraic maneuvers, of the same type used in solving linear and quadratic polynomial equations (example shown, in a moment).

Has it been awhile, since you've done algebra?

Most trigonometry texts are written with an assumption that algebra is a prerequisite; therefore, the authors do not generally go over the algebra. You're expected to have the following skill.

Solve for x:

2x^2 = x

Subtract x

2x^2 - x = 0

Factor

x(2x - 1) = 0

Zero-Product Property

x = 0

or

2x - 1 = 0

x = 1/2

Do you "see" the symbolic similarity? Replace the symbol x above with the symbol sin(x), and the steps are exactly the same as the steps to set up that trig version of yours.

In your exercises, the set-up is basically trying to manipulate the given equation into single trig expressions equal to some Real numbers (except for the ones that require you to be familiar with the introductory identities). We often use algebra to do this, just like we use algebra to isolate x, when solving polynomial equations.