Don't understand how eqn 2 was reached from eqn 1.

  • Thread starter Tlark10
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In summary, the conversation discusses finding solutions to a question involving equations and integration. One person suggests setting x equal to cos(theta) and using the identity sin^2(theta) + cos^2(theta) = 1 to simplify the equations and find the desired solution. Another person advises looking for similarities between the two equations to determine the value of x.
  • #1
Tlark10
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moved from general forum so homework template is missing
I have found solutions to a question I am trying to figure out, and I am unsure how they got from one step to the next. Is it some sort of integration??

Eqn 1) 0.625 = sin(theta) - 0.5cos(theta)

Eqn 2) 0.625 = sqrt(1 - x^2) - 0.5x
 
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  • #2
Just let ##x=\cos \theta.## Then by ##\sin^2 \theta+\cos^2 \theta =1,## you can get what you want.
 
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Likes Nipuna Weerasekara and Tlark10
  • #3
tommyxu3 said:
Just let ##x=\cos \theta.## Then by ##\sin^2 \theta+\cos^2 \theta =1,## you can get what you want.
I second this. Next time just look at the two equations and try to see any resemblance. Then you might find some. In here you might see x=Cos(theta) directly whereas you might see Sin(theta)= SqRt(1-x^2).
 

1. How do you solve for a variable in an equation?

To solve for a variable in an equation, you can use algebraic manipulation. This involves performing the same operation on both sides of the equation to isolate the variable on one side.

2. What is the difference between equations and expressions?

An equation is a mathematical statement with an equals sign, while an expression is a combination of numbers, variables, and operations. Equations can be solved to find the value of a variable, while expressions cannot.

3. What is the order of operations in equations?

The order of operations in equations follows the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

4. How do you check if your solution to an equation is correct?

To check if your solution to an equation is correct, you can substitute the value of the variable into the original equation and see if it satisfies the equation. If it does, then your solution is correct.

5. Can you explain the process of solving a multi-step equation?

To solve a multi-step equation, you need to use the order of operations and perform the same operation on both sides of the equation to isolate the variable. This may involve using inverse operations to undo any operations that are being performed on the variable. The goal is to get the variable by itself on one side of the equation.

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