How Do You Solve the Equation 20sin(t)cos(t) = -4cos(t) for t?

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In summary, the conversation is about solving the equation 20sin(t)cos(t)=-4cos(t), with the individual unsure of what to do and their instructor not providing enough guidance. The suggested next step is to factor the equation.
  • #1
nickb145
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Homework Statement


20sin(t)cos(t)=-4cos(t)



Homework Equations





The Attempt at a Solution



I added the cos to the other side but I am kind of stuck what to do. My instructor never really went over this well enough. Ugh..
 
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  • #2
nickb145 said:

Homework Statement


20sin(t)cos(t)=-4cos(t)



Homework Equations





The Attempt at a Solution



I added the cos to the other side but I am kind of stuck what to do. My instructor never really went over this well enough. Ugh..

I don't see any question. What is the problem? Solving for ##t##? If so, after you do that first step, factor it.
 

Related to How Do You Solve the Equation 20sin(t)cos(t) = -4cos(t) for t?

1. What is the purpose of solving for T sin and cos?

The purpose of solving for T sin and cos is to find the value of T in a trigonometric equation. T represents the period or time it takes for a trigonometric function to complete one full cycle. By solving for T, we can determine the frequency and other important characteristics of the function.

2. How do I solve for T sin and cos?

To solve for T sin and cos, you will need to use trigonometric identities and equations. First, identify the given information such as the amplitude, phase shift, and frequency. Then, use the appropriate formula (such as T = 2π/frequency) to solve for T. You may also need to use algebraic manipulation to isolate T on one side of the equation.

3. Can I use a calculator to solve for T sin and cos?

Yes, you can use a calculator to solve for T sin and cos. Most scientific calculators have trigonometric functions and inverse trigonometric functions, making it easier to solve for T. However, it is important to understand the steps and concepts behind solving for T in order to use the calculator effectively.

4. What is the difference between solving for T sin and T cos?

The difference between solving for T sin and T cos lies in the trigonometric function being used. T sin represents the period of a sine function, while T cos represents the period of a cosine function. The two functions have different characteristics and can have different values for T, even if they have the same frequency.

5. Are there any special cases when solving for T sin and cos?

Yes, there are some special cases when solving for T sin and cos. If the function has a phase shift or is in a different form (such as a tangent function), the formula for T may be different. It is important to be familiar with different trigonometric identities and equations in order to solve for T correctly in these special cases.

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