Best way to solve equations like that

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In summary, the conversation is about solving a physics equilibrium problem involving the equation 900cos(x)+600cos(45+x) = 0, with the angles given in degrees. The speaker is seeking advice on the best way to analytically solve the equation, having already tried using sum-difference formulas without success. Another person suggests expanding the cos(45+x) term, substituting cosx with t and solving for t, then considering the permissible values of t within the range of [-1,1].
  • #1
fishingspree2
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Im doing a physics equilibrium problem and I need to solve this equation:

900cos(x)+600cos(45+x) = 0

(the angles are in degrees)

What would be the best way to analytically solve this kind of equation? I tried using the sum-difference formulas but it wasn't able to solve for x.

Thank you very much
 
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  • #2
well the question is essentially only in one variable x

so instead of adding them what u do is , expland the cos(45+x) term

then put cosx=t and sinx whill be sqrt(1-t^2)

and solve the q in t

and then look at the permissible values of t

since t belongs to [-1,1]
 

FAQ: Best way to solve equations like that

What is the general process for solving equations?

The general process for solving equations involves isolating the variable on one side of the equation and simplifying both sides until the variable is alone and can be solved for. This can be done by using inverse operations, such as addition and subtraction, multiplication and division, and exponent operations.

How do I know which operations to use when solving equations?

The operations used to solve equations depend on the specific equation and the goal of solving it. However, the general rule is to use inverse operations to cancel out the operations that are being done to the variable. For example, if the variable is being multiplied by a number, use division to cancel it out.

What should I do if there are variables on both sides of the equation?

If there are variables on both sides of the equation, the first step is to combine like terms on each side to simplify the equation. Then, isolate the variable on one side using inverse operations. Finally, solve for the variable by simplifying both sides of the equation until it is alone.

Are there any shortcuts for solving equations?

There are some shortcuts that can be used for solving certain types of equations, such as using the quadratic formula for solving quadratic equations or using the distributive property to simplify expressions. However, it is important to understand the general process for solving equations as these shortcuts may not always be applicable.

How do I check if my solution is correct?

To check if your solution is correct, you can substitute the value you found for the variable back into the original equation and see if it makes the equation true. If it does, then your solution is correct. You can also use a calculator or graphing software to graph the equation and see if the solution falls on the graph.

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