Really simple system of equations

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SUMMARY

The discussion centers on solving a system of equations involving trigonometric functions to find the angle \Phi and the tension Tac. The equations presented are 2500 - Tac cos \Phi = 0 and Tac sin \Phi - 500 = 0. The user successfully derived Tac = 500/sin \Phi and reformulated the first equation to 2500 - 500cos \Phi/sin \Phi = 0. The target solution is confirmed to be 11.31° for \Phi, but further steps to solve for Tac are needed.

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yoleven
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Homework Statement


1. 2500-Tac cos [tex]\Phi=0[/tex]
2. Tac sin[tex]\Phi-500=0[/tex]

Homework Equations





The Attempt at a Solution


I have 2 equations. I need to solve for [tex]\Phi[/tex] to get Tac. I have got to the point of :
Tac=500/sin[tex]\Phi[/tex]
2500-500/sin[tex]\Phi*(cos\Phi)=0[/tex]

after this i can't go any further

I am looking at the solution of 11.31°. But I need to solve to get it.
 
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yoleven said:
I have got to the point of :
Tac=500/sin[tex]\Phi[/tex]
2500-500/sin[tex]\Phi*(cos\Phi)=0[/tex]

after this i can't go any further

I am looking at the solution of 11.31°. But I need to solve to get it.

Hi yoleven! :smile:

(have a phi: φ :smile:)

Your second line should be 2500 - 500cosφ/sinφ = 0. :wink:
 

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