# Solve E^x = k/c sin^2(x) Homework

• squaremeplz
This is why the calculator is adding the extra terms.In summary, the conversation is discussing the equation e^x = k/c * sin^2(y) and solving for t. The person initially thought the solution was t=arcsin(sqrt(ce^x/k)), but their calculator is giving a different answer with additional terms. The person questions whether y should be t instead or if y is a function of t. The other person explains that y can take on multiple values due to the periodic nature of sine, resulting in the calculator's answer.
squaremeplz

## Homework Statement

$$e^x = \frac {k}{c}sin^2(y)$$ solving for t

i thought it was $$t=arcsin(\sqrt{\frac{ce^x}{k}})$$

but my calc is saying like the answer above + ln4*pi + pi.

er, where is there a "t" in your expression? do you mean t instead of y? or is y a function of t? if the y is supposed to be a t, you are most certainly right, otherwise, we are missing information

## Homework Statement

$$e^x = \frac {k}{c}sin^2(y)$$ solving for t

i thought it was $$t=arcsin(\sqrt{\frac{ce^x}{k}})$$

but my calc is saying like the answer above + ln4*pi + pi.
$$y= arcsin(\sqrt{\frac{ce^x}{k}}))$$
is a solution buy sine is a periodic function so there are other values of y that will give the same value.

## 1) What does the equation E^x = k/c sin^2(x) represent?

The equation E^x = k/c sin^2(x) represents the relationship between the exponential function and the sine function with a coefficient of k/c. It is a mathematical expression used to solve for the value of x.

## 2) How do I solve E^x = k/c sin^2(x)?

To solve this equation, you can use logarithms or algebraic manipulation to isolate the variable x. You may also use a calculator to solve for the numerical value.

## 3) What are the possible solutions for E^x = k/c sin^2(x)?

The possible solutions for this equation are all real numbers, as both the exponential and sine functions can take on any real value. However, depending on the values of k and c, the equation may have multiple or no solutions.

## 4) Can this equation be solved using a graphing calculator?

Yes, this equation can be solved using a graphing calculator by graphing both sides of the equation and finding the points of intersection. The x-value of the intersection point will be the solution to the equation.

## 5) How is the equation E^x = k/c sin^2(x) applicable in real life?

This equation can be used in various scientific and mathematical fields to model exponential and sine relationships. For example, it can be used in population growth models, electrical circuit analysis, or even in predicting the behavior of waves.

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