13. I An electrical circuit alternating current is modeled by = 15 cos ( 120 t + п/2), where 0 ≤ t ≤ 1/30 and I is in amperes. Find the frequency of that current.
13. I An electrical circuit alternating current is modeled by = 15 cos ( 120 t + п/2), where 0 ≤ t ≤ 1/30 and I is in amperes. Find the frequency of that current.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.5: Trigonometric Graphs
Problem 18E
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![**Problem 13:**
An electrical circuit's alternating current is modeled by the equation:
\[ I = 15 \cos(120\pi t + \pi/2), \]
where \( 0 \leq t \leq 1/30 \) and \( I \) is in amperes. Determine the frequency of this current.
**Explanation:**
The equation describes a cosine function that models the alternating current. The angular frequency (\( \omega \)) is given as \( 120\pi \). The frequency (\( f \)) of the alternating current can be found using the relation:
\[ \omega = 2\pi f. \]
From this equation, we can solve for the frequency \( f \):
\[ f = \frac{\omega}{2\pi} = \frac{120\pi}{2\pi} = 60 \text{ Hz}. \]
Thus, the frequency of the current is 60 Hertz.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2816e768-d46c-42f8-b287-986238abcd2a%2F7d3f9a60-d04f-4728-af24-1314f40db2cc%2Fl2dldn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 13:**
An electrical circuit's alternating current is modeled by the equation:
\[ I = 15 \cos(120\pi t + \pi/2), \]
where \( 0 \leq t \leq 1/30 \) and \( I \) is in amperes. Determine the frequency of this current.
**Explanation:**
The equation describes a cosine function that models the alternating current. The angular frequency (\( \omega \)) is given as \( 120\pi \). The frequency (\( f \)) of the alternating current can be found using the relation:
\[ \omega = 2\pi f. \]
From this equation, we can solve for the frequency \( f \):
\[ f = \frac{\omega}{2\pi} = \frac{120\pi}{2\pi} = 60 \text{ Hz}. \]
Thus, the frequency of the current is 60 Hertz.
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