Kaleigh's question at Yahoo Answers involving eliminating a parameter

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In summary, the equation in the xy-plane whose graph includes x = cos t and y = sec t is y = 1/x. This can be found by multiplying the two parametric equations together and eliminating the parameter t. Other questions about parametric equations can be posted in the forum provided in the link.
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Hello Kaleigh,

We are given the parametric equations:

\(\displaystyle x=\cos(t)\)

\(\displaystyle y=\sec(t)\)

One way we may eliminate the parameter $t$ is to multiply the two equations together, giving:

\(\displaystyle xy=1\)

We may choose to write this as:

\(\displaystyle y=\frac{1}{x}\)

To Kaleigh and any other guests viewing this topic, I invite and encourage you to post other parametric equations questions in our http://www.mathhelpboards.com/f21/ forum.

Best Regards,

Mark.
 

Related to Kaleigh's question at Yahoo Answers involving eliminating a parameter

1. How do you eliminate a parameter in a scientific equation?

In order to eliminate a parameter in a scientific equation, you must first identify which variable is the parameter. Then, you can substitute that variable with its actual value or solve for it in terms of the other variables in the equation.

2. Why is it important to eliminate parameters in scientific equations?

Eliminating parameters in scientific equations can help simplify the equation and make it easier to analyze and understand. It also allows for more accurate predictions and calculations.

3. Can you provide an example of eliminating a parameter in a scientific equation?

Sure, let's say we have the equation y = mx + b, where m is the slope and b is the y-intercept. To eliminate the parameter b, we can solve for it by substituting in the coordinates of a point on the line. So if we have the point (2, 5), we can plug in x = 2 and y = 5 to get 5 = 2m + b. Solving for b, we get b = 5 - 2m. We can now substitute this value for b in the original equation to eliminate the parameter.

4. What are some common methods for eliminating parameters in scientific equations?

Some common methods for eliminating parameters include substitution, solving for the parameter in terms of other variables, and using properties of logarithms or exponentials.

5. Are there any situations where eliminating a parameter is not possible?

Yes, there are some equations where it may not be possible or practical to eliminate a parameter. This could be due to the complexity of the equation or the inability to solve for the parameter in terms of other variables. In these cases, it may be necessary to use numerical methods or approximations to solve the equation.

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