Calc 3 Factoring a Trig equation

Thread starter lukasz08
Start date Oct 21, 2008
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Calc 3 Factoring Trig

In summary, factoring a trigonometric equation in Calc 3 is done to simplify the equation and make it easier to solve. The steps involved are identifying common terms, using trigonometric identities, factoring out common terms, and solving for the remaining variable(s). This process can lead to extraneous solutions, so it is important to check the solutions obtained. Some common trigonometric identities used in factoring are Pythagorean identities, double angle identities, and sum and difference identities. Factoring can also be used to solve for multiple variables, but it is important to check the solutions to ensure they are valid for the original equation.

Oct 21, 2008

lukasz08

can you somehow factor the following equation ? sqrt(9sin^2(t)+16cos^2(t)+1/4)

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Oct 21, 2008

mathman

Science Advisor

Using sin^2 + cos^2 =1, you can simplify the expression inside the sqrt in 2 ways (cos^2 only or sin^2 only with + constant for either). Try it and see if you can do something with it.

What is the purpose of factoring a trigonometric equation in Calc 3?

The purpose of factoring a trigonometric equation in Calc 3 is to simplify the equation and make it easier to solve. By factoring out common terms, the equation can be transformed into a more manageable form.

What are the steps to factor a trigonometric equation in Calc 3?

The steps to factor a trigonometric equation in Calc 3 are as follows:

Identify common terms or factors in the equation
Use trigonometric identities to rewrite the equation in terms of those common terms
Factor out the common terms
Solve for the remaining variable(s)

Can factoring a trigonometric equation in Calc 3 lead to extraneous solutions?

Yes, factoring a trigonometric equation in Calc 3 can lead to extraneous solutions. This is because factoring can introduce additional solutions that do not satisfy the original equation. It is important to check the solutions obtained after factoring to ensure they are valid for the original equation.

What are the common trigonometric identities used in factoring a trigonometric equation in Calc 3?

Some common trigonometric identities used in factoring a trigonometric equation in Calc 3 are:

Pythagorean identities: sin²x + cos²x = 1 and tan²x + 1 = sec²x
Double angle identities: sin2x = 2sinx cosx and cos2x = cos²x - sin²x
Sum and difference identities: sin(x ± y) = sinx cosy ± cosx siny and cos(x ± y) = cosx cosy ∓ sinx siny

Can factoring a trigonometric equation in Calc 3 be used to solve for multiple variables?

Yes, factoring a trigonometric equation in Calc 3 can be used to solve for multiple variables. This is because factoring can simplify the equation and make it easier to isolate and solve for different variables. However, it is important to check the solutions obtained to ensure they satisfy the original equation.