# Homework Help: How do I solve for theta?

1. Mar 5, 2010

### Ryuk1990

1. The problem statement, all variables and given/known data

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

2. Relevant 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.

3. 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.

2. Mar 5, 2010

### Staff: Mentor

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?

3. Mar 5, 2010

### rock.freak667

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

Then remember that sin2θ+cosθ=1.

so something like R2sin2θ+R2cos2θ=1

4. Mar 5, 2010

### Ryuk1990

Do you mean as in like this?

tan(theta) = 200/400

Is this legal?

5. Mar 5, 2010

### 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.

6. Mar 6, 2010

### Staff: Mentor

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.