Question
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
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Answer
The first period of the graph of \( y = \cos(x) \) starts at \( y = 1 \).
Solution
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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Simplify this solution 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!
