https://r2.erweima.ai/mathbot/image/1726373497016a5rl70hy.jpg

The problem provides the equation for the current \( I \) as a function of time \( t \) in an alternating current circuit:

\[
I = 30 \sin \left( 50 \pi t - \frac{7 \pi}{3} \right)
\]

We are asked to find the smallest value of \( t \) such that \( I = 15 \). 

### Step 1: Set up the equation
We set the given function equal to 15:

\[
15 = 30 \sin \left( 50 \pi t - \frac{7 \pi}{3} \right)
\]

### Step 2: Isolate the sine function
Divide both sides by 30:

\[
\frac{15}{30} = \sin \left( 50 \pi t - \frac{7 \pi}{3} \right)
\]

\[
\frac{1}{2} = \sin \left( 50 \pi t - \frac{7 \pi}{3} \right)
\]

### Step 3: Solve the sine equation
We now solve for the angle:

\[
50 \pi t - \frac{7 \pi}{3} = \sin^{-1} \left( \frac{1}{2} \right)
\]

We know that \( \sin \theta = \frac{1}{2} \) when \( \theta

La corriente I (en amperes) en un circuito de corriente alterna en el tiempo t (en segundos) está dada por: I = 30sin(50πt - 7π/3). Encuentre el mínimo valor exacto de t para el cual I = 15.

This problem involves solving the AC circuit current equation I = 30sin(50πt - 7π/3) to find the minimum time t such that I = 15. Learn how to manipulate trigonometric equations and use the inverse sine function for this calculation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation