Pregunta
The first period of the graph of \( y=\cos (x) \) starts at \( y= \) \( \qquad \) a 0 b -1 C 1 d \( \pi \) e \( 2 \pi \) Check It
Ask by Pollard Carroll. in the United States
Feb 27,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The first period of the graph of \( y = \cos(x) \) starts at \( y = 1 \).
Solución
To determine where the first period of the graph of \( y = \cos(x) \) starts, we need to understand the properties of the cosine function.
1. The cosine function \( y = \cos(x) \) has a maximum value of 1 and a minimum value of -1.
2. The function starts at its maximum value when \( x = 0 \), which means \( y = \cos(0) = 1 \).
3. The period of the cosine function is \( 2\pi \), meaning it repeats every \( 2\pi \) units.
Given these points, the first period of the graph of \( y = \cos(x) \) starts at \( y = 1 \) when \( x = 0 \).
Thus, the correct answer is:
**C 1**
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Como
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Mind Expander
The first period of the graph of \( y = \cos(x) \) starts at \( y = 1 \). The cosine function begins at its maximum value of 1 when \( x = 0 \). This makes option C the correct answer. In terms of its periodic behavior, the cosine function completes one full cycle from \( 0 \) to \( 2\pi \). During this cycle, the graph oscillates from 1 (the maximum) to -1 (the minimum) and back, illustrating the beautiful symmetry of trigonometric functions!
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