Solving for Theta: A Physics-Math Dilemma

[Ryuk1990]

Homework Statement

This is originally from a physics problem but it's more of a math question. How do I solve for theta?

Homework Equations

400 - Tcos(theta) = 0

-200 + Tsin(theta) = 0

Using those equations, I need to solve for theta. Also, knowing that tan(theta) = sin(theta)/cos(theta) is supposed to be relevant to this.

The Attempt at a Solution

All I did was simplify the equations to 200 - Tcos(theta) + Tsin(theta) = 0

Not sure if that was a good idea or not but I'm suck.

 

[Mark44]

Homework Statement

This is originally from a physics problem but it's more of a math question. How do I solve for theta?

Homework Equations

400 - Tcos(theta) = 0

-200 + Tsin(theta) = 0

Using those equations, I need to solve for theta. Also, knowing that tan(theta) = sin(theta)/cos(theta) is supposed to be relevant to this.

The Attempt at a Solution

All I did was simplify the equations to 200 - Tcos(theta) + Tsin(theta) = 0

Not sure if that was a good idea or not but I'm suck.

Your equations can be rewritten as
Tsin(theta) = 200
Tcos(theta) = 400

Instead of adding equations to each other, what about dividing each side of one equation by the corresponding side of the other?

 

[rock.freak667]

Place all the constants on one side of the equality for each of the equations.

Then remember that sin²θ+cos^θ=1.

so something like R²sin²θ+R²cos²θ=1

 

[Ryuk1990]

Your equations can be rewritten as
Tsin(theta) = 200
Tcos(theta) = 400

Instead of adding equations to each other, what about dividing each side of one equation by the corresponding side of the other?

Do you mean as in like this?

tan(theta) = 200/400

Is this legal?

 

[Mentallic]

Yes

You can even take a slower approach to solve the two simultaneous equations:

$$Tsin\theta=200$$ (1)

$$Tcos\theta=400$$ (2)

Re-arrange (1) : $$T=200csc\theta$$ (3)

Substitute (3) into (2) : $$200csc\theta cos\theta=400$$

Simplify : $$tan\theta=1/2$$

So yes, if you are convinced that substitution is a valid step in solving simultaneously, then the process of dividing both equations together is also.

 

[Mark44]

Do you mean as in like this?

tan(theta) = 200/400

Is this legal?

Sure, it's legal, as long as T isn't 0, and I'm reasonably sure in this problem it isn't. Once you get a value for theta, then substitute into either of the original equations to find T.