Solving cosz=2: A Logarithmic Approach

Thread starter kathrynag
Start date Mar 10, 2009
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Approach Logarithmic

In summary, to solve the equation cosz=2, we can use the inverse of the cosine function, which is the arccosine function, and then use logarithms to isolate and solve for z. A logarithmic approach is useful because it simplifies the equation and allows us to solve for variables inside the trigonometric functions. An example of using logarithms to solve cosz=2 is taking the arccosine of both sides and using the logarithmic property to rewrite it as log(base 10) 2. The main difference between using logarithms and trigonometric identities is that logarithms can solve for variables inside the functions, while identities can only manipulate the expressions within the functions. However, a limitation of

Mar 10, 2009

kathrynag

Homework Statement

Sove cosz=2

Homework Equations

The Attempt at a Solution

I need to solve this, but am not quite sure how. I was told to use log.

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Mar 11, 2009

lanedance

Homework Helper

Hi kathrynag welcome to pf

i assume you're working with complex numbers...

does the complex expression of cos help
[tex]\cos{z} = \frac{e^{iz}+e^{-iz}}{2}[/tex]

FAQ: Solving cosz=2: A Logarithmic Approach

1. How do you solve cosz=2 using logarithms?

To solve this equation, we can use the inverse of the cosine function, which is the arccosine function. This function can be written as cos^-1. By taking the arccosine of both sides of the equation, we can isolate z and solve for it using logarithms.

2. Why is a logarithmic approach useful for solving this equation?

A logarithmic approach is useful because it allows us to solve for variables that are inside the trigonometric functions. In this case, we can use the property of logarithms that states log(base a) a = 1 to simplify the equation and solve for z.

3. Can you provide an example of using logarithms to solve cosz=2?

Sure, let's say we have the equation cosz=2. We can take the arccosine of both sides to get z = arccos(2). Then, using the logarithmic property, we can rewrite this as z = log(base 10) 2. This gives us the solution z = 0.301.

4. What is the difference between using logarithms and using trigonometric identities to solve this equation?

The main difference is that using logarithms allows us to solve for variables that are inside the trigonometric functions, while using trigonometric identities can only be used to manipulate the expressions within the functions. Using logarithms also simplifies the equation and makes it easier to solve.

5. Are there any limitations to using a logarithmic approach to solve this equation?

Yes, there are some limitations. Logarithms can only be used to solve equations that have a variable inside the trigonometric functions. If the variable is outside the function, then other methods such as using trigonometric identities would be more suitable for solving the equation.