To find the period of the function \( E = 2\cos(90\pi t) \), follow these steps:

### Step 1: Understand the General Form
The general form of a cosine function is:
\[
y = A \cos(Bt + C) + D
\]
where:
- \(A\) is the amplitude,
- \(B\) affects the period,
- \(C\) is the phase shift, and
- \(D\) is the vertical shift.

The period \(T\) of the function is given by:
\[
T = \frac{2\pi}{|B|}
\]

### Step 2: Identify the Coefficient \(B\)
In your equation \( E = 2\cos(90\pi t) \), the coefficient \(B\) is \(90\pi\).

### Step 3: Calculate the Period
Using the formula for the period:
\[
T = \frac{2\pi}{|90\pi|} = \frac{2\pi}{90\pi} = \frac{2}{90} = \frac{1}{45}
\]

### Final Answer:
The period of the function \( E = 2\cos(90\pi t) \) is \(\frac{1}{45}\).

Would you like more details on how to handle trigonometric functions or have any questions? Here are some related questions:

1. What is the amplitude of the function \( E = 2\cos(90\pi t) \)?
2. How does changing the coefficient \(B\) affect the period of a trigonometric function?
3. What are the phase shift and vertical shift for this function?
4. How would the period change if the function was \( \cos(45\pi t) \) instead?
5. Can you describe the graph of \( E = 2\cos(90\pi t) \) over one period?

**Tip:** Always remember that the period of a cosine or sine function depends only on the coefficient of \(t\) inside the function.

Learn how to find the period of the function E = 2 cos(90πt) step-by-step. Understand the cosine function's period formula and apply it to solve for the period of this specific trigonometric function. Suitable for advanced high school students and anyone interested in trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation