Solving Trigonometry Problem: 2 Variables, 2 Equations

[Champ07]

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

 

[arildno]

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

 

[Champ07]

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

 

[HallsofIvy]

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 x^2+ y^2= 1. What happens if you add the first two equations?

 

[nicktacik]

HallsofIvy how do you get those equations?

Seems it should be
<br /> 3 = 1.2x + v\frac{\sqrt{3}}{2}
0 = 1.2y - 0.5v
x^2 + y^2 = 1<br />

 

[HallsofIvy]

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)= \sqrt{2}/3 and sin(30)= 1/2.

 

[AlephZero]

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.

 

[rocomath]

i just solved it, long prob