Solving simultaneous trigonometric equations

[LogoHeli]

Hi there,

I'm having a little trouble solving for what is essentially 2 unkonws in the equations (i am trying to solve for w and ?):

40 - w .sin(?) = 0 AND
69.28 - w - w.cos(?)

It has really gotten me stumped..i've tried reaarranging to put the w's and the trig functions on one side, then tried to manipulate from there to no avail. Ive trie solving simultaneously by dividing cos by sin equalling tan --> thus cancelling ? and a set of w's. leaving 40/69.28 = 1/w . tan

..however i dont think any of the approaches i am using are mathematically correct ...any help would be greatly appreciated.

thanks in advanced,
lawrence

 

[Deleted member 4993]

Hi there,

I'm having a little trouble solving for what is essentially 2 unkonws in the equations (i am trying to solve for w and ?):

40 - w .sin(?) = 0 AND
69.28 - w - w.cos(?) <<< This is not an equation - where is the "=" sign?

It has really gotten me stumped..i've tried reaarranging to put the w's and the trig functions on one side, then tried to manipulate from there to no avail. Ive trie solving simultaneously by dividing cos by sin equalling tan --> thus cancelling ? and a set of w's. leaving 40/69.28 = 1/w . tan

..however i dont think any of the approaches i am using are mathematically correct ...any help would be greatly appreciated.

thanks in advanced,
lawrence

from equation (1)

w cos(?) = ±?(w²-1600) .................edited

Use that in equation (2) to eliminate ? - then solve for w and eventually ?.

 

[LogoHeli]

Thank you for your prompt response.
i was just wondering where you got w cos(?) = ±?(1600 - w²) from?
btw i meant 69.28 - w - w.cos(?) = 0

 

[Deleted member 4993]

Thank you for your prompt response.
i was just wondering where you got w cos(?) = ±?(w² - 1600) from? <<< there was a typo

as I stated in my response "from equation (1)"

40 - w .sin(?) = 0 ................(1)

w .sin(?) = 40

w² .sin²(?) = 1600.... and so on...



btw i meant 69.28 - w - w.cos(?) = 0