How do I solve for theta?

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In summary, to solve for theta in this math problem, you can rewrite the given equations as Tsin(theta) = 200 and Tcos(theta) = 400. You can then divide one equation by the other to get tan(theta) = 200/400. Alternatively, you can use substitution to solve the simultaneous equations and find that tan(theta) = 1/2. Either method is valid and will give you a value for theta, which can then be used to find the value of T.
  • #1
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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.
 
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  • #2
Ryuk1990 said:

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?
 
  • #3
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
Mark44 said:
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?
 
  • #5
Yes :smile:

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

[tex]Tsin\theta=200[/tex] (1)

[tex]Tcos\theta=400[/tex] (2)

Re-arrange (1) : [tex]T=200csc\theta[/tex] (3)

Substitute (3) into (2) : [tex]200csc\theta cos\theta=400[/tex]

Simplify : [tex]tan\theta=1/2[/tex]

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
Ryuk1990 said:
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.
 

1. How do I solve for theta using trigonometric functions?

To solve for theta using trigonometric functions, you will need to use the inverse trigonometric functions such as sin^-1, cos^-1, and tan^-1. These functions will help you find the angle measure of theta when given the ratio of two sides of a right triangle.

2. What is the difference between solving for theta in degrees and radians?

When solving for theta in degrees, the angle measure will be given in degrees (°), which is a unit of measurement for angles. However, when solving for theta in radians, the angle measure will be given in radians (rad), which is a unit of measurement for angles based on the radius of a circle.

3. How do I solve for theta using the Law of Sines?

To solve for theta using the Law of Sines, you will need to have two angle measures and one side length of a triangle. Then, you can use the formula sin(theta)/a = sin(alpha)/b to solve for the missing angle measure theta.

4. What is the Pythagorean Theorem and how does it help solve for theta?

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem can be used to solve for theta by finding the missing side length using the equation c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

5. Can I use a calculator to solve for theta?

Yes, you can use a calculator to solve for theta. Most scientific calculators have the trigonometric functions and inverse trigonometric functions built in, making it easier to solve for theta. However, it is important to make sure your calculator is set to the correct unit of measurement (degrees or radians) before solving for theta.

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