Solving Trigonometry Problem: 2 Variables, 2 Equations

In summary, the conversation is about a two variable trigonometry question with two equations. The person is unsure if the equations are simultaneous and is asking for help in solving for the values of x and v. They mention using the summation formula and substituting values, but are unsure of their approach. Another user suggests using x = cos(x) and y = sin(x) and adding the two equations together. The conversation ends with the person saying they have solved the problem.
  • #1
Champ07
11
0
I've been really stumped by this one from my math class. It's a two variable trig. question with two equations. I believe there simultaneous but I'm not sure

3 = 1.2(cosx) + v(cos30)
0 = 1.2(sinx) - v(sin30)

Solve for the values of x & v

Please explain how you got your answer or show work. Thanks
 
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  • #2
Well, solve for v first from, say, the 2nd eq.
Then you get a trig equation; use the summation formula to reshape it so that you can solve for relevant x's
 
  • #3
Sorry I'm not familar with the summation formula. I solved for V in the second equation and got V = .6sinx.

I substituted that into the second equation and got sin = 0, 180 or 360 but then the 2nd equation doesn't check out. I know I'm doing it wrong somehow just not sure how
 
  • #4
Champ07 said:
I've been really stumped by this one from my math class. It's a two variable trig. question with two equations. I believe there simultaneous but I'm not sure

3 = 1.2(cosx) + v(cos30)
0 = 1.2(sinx) - v(sin30)

Solve for the values of x & v

Please explain how you got your answer or show work. Thanks
Actually, I suspect the problem asked YOU to explain how you got your answer or shiow work. I don't have to! Let x= cos(x) and y= sin(x). then you have the two equations
3= 1.2x+ vy and 0 = 1.2x+ vy as well as the obvious equation [itex] x^2+ y^2= 1[/itex]. What happens if you add the first two equations?
 
  • #5
HallsofIvy how do you get those equations?

Seems it should be
[tex]
3 = 1.2x + v\frac{\sqrt{3}}{2}[/tex]
[tex]0 = 1.2y - 0.5v[/tex]
[tex]x^2 + y^2 = 1
[/tex]
 
  • #6
How did I get those two equations? I copied them from the first post in this thread!
3 = 1.2(cosx) + v(cos30)
0 = 1.2(sinx) - v(sin30)
I now see, looking more closely, that it might be good idea to multiply the first equation by sin(30) and the second equation by cos(30). Although it wasn't said, I assume that is "30 degrees" so that cos(30)= [itex]\sqrt{2}/3[/itex] and sin(30)= 1/2.
 
  • #7
Champ07 said:
Sorry I'm not familar with the summation formula. I solved for V in the second equation and got V = .6sinx.

That's the right idea, but the solution to 0 = 1.2(sinx) - v(sin30) = 1.2(sinx) -v(0.5) isn't v = 0.6 sin x.
 
  • #8
i just solved it, long prob
 

1. What is the purpose of solving trigonometry problems with 2 variables and 2 equations?

The purpose of solving trigonometry problems with 2 variables and 2 equations is to find the values of the two unknown variables in the given equations. This can help us to better understand and analyze geometric and real-world situations where multiple variables are involved.

2. What are the basic steps for solving a trigonometry problem with 2 variables and 2 equations?

The basic steps for solving a trigonometry problem with 2 variables and 2 equations are:

  1. Identify the two unknown variables in the equations.
  2. Use trigonometric identities and properties to manipulate the equations and eliminate one of the variables.
  3. Substitute the value of the eliminated variable into one of the equations to solve for the remaining variable.
  4. Use the solved variable to find the value of the previously eliminated variable.
  5. Check your solution by substituting the values into both equations to ensure they are satisfied.

3. What are some common trigonometric identities used in solving problems with 2 variables and 2 equations?

Some common trigonometric identities used in solving problems with 2 variables and 2 equations include:

  • Pythagorean identities: sin2(x) + cos2(x) = 1 and tan2(x) + 1 = sec2(x)
  • Sum and difference identities: sin(x ± y) = sin(x)cos(y) ± cos(x)sin(y) and cos(x ± y) = cos(x)cos(y) ∓ sin(x)sin(y)
  • Double angle identities: sin(2x) = 2sin(x)cos(x) and cos(2x) = cos2(x) − sin2(x)

4. How can I check my solution for a trigonometry problem with 2 variables and 2 equations?

You can check your solution by substituting the values of the variables into both equations and ensuring that they are satisfied. If both equations are true when the values are substituted, then your solution is correct.

5. Can I use a calculator to solve a trigonometry problem with 2 variables and 2 equations?

Yes, you can use a calculator to solve a trigonometry problem with 2 variables and 2 equations. However, it is important to have a good understanding of the trigonometric identities and how to apply them in order to use the calculator effectively. It is also important to double check your solution by hand to ensure accuracy.

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