How Do You Solve These Trigonometric Equations for Relative Motion?

[weedannycool]

Homework Statement

i have 2 equations:

400cos $$\vartheta$$_a = 300 + V_acos45

and

400sin $$\vartheta$$_a = V_asin45

Homework Equations

The Attempt at a Solution

i have no clue, maybe square it.

thanks

 

[tiny-tim]

Hi weedannycool!

… maybe square it.

Yes, of course …

what do you get? ​

 

[Mark44]

Also, you should replace cos45 and sin45 by sqrt(2)/2. I'm assuming the angles are in degrees.

One other thing. Instead of starting a new thread for essentially the same (but corrected) problem, you should continue the old thread, putting in the corrected set of equations.

 

[weedannycool]

right so i have the to equations squared. not positive with what i should to next though. is there a method for solving these.

thanks for the help so far

 

[Mark44]

Do you know any identities involving the sum of the squares of the sine and cosine functions?

 

[RTW69]

Mark44's approach replacing sin45 and cos45 with sqrt(2)/2 seems the most straight forward approach. You have 2 equations with 2 unknowns, theta-a and Va. The expression with Va*sqrt(2)/2 in the second equation can be substituted into the first equation. You are left with one equation with one unknown, theta-a. Trial and error to find theta-a. Plug theta-a into either equation to find Va. Theta-a will be in degrees, Va won't be.

 

[weedannycool]

thanks guys. relative motion is a blast.