Question
The graph of \( \sin (x+c) \) is shifted \( \frac{3 \pi}{2} \) units to the left compared to \( \sin x \). What is the value of \( c \) ? (1 point) \( c=\square \)
Ask by O'Quinn Hodges. in the United States
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( c = -\frac{3\pi}{2} \)
Solution
To find the value of \( c \) in the given scenario, we need to understand how the graph of \( \sin(x+c) \) is shifted compared to the graph of \( \sin(x) \).
The general form of the sine function is \( \sin(x+c) \), where \( c \) represents the phase shift of the function. A positive value of \( c \) shifts the graph to the left, while a negative value of \( c \) shifts the graph to the right.
Given that the graph of \( \sin(x+c) \) is shifted \( \frac{3\pi}{2} \) units to the left compared to \( \sin(x) \), we can determine the value of \( c \) by setting up an equation based on the phase shift.
The phase shift of \( \sin(x+c) \) is given by \( c \), and the phase shift of \( \sin(x) \) is 0. Since the graph of \( \sin(x+c) \) is shifted \( \frac{3\pi}{2} \) units to the left, we can set up the equation:
\[ c = -\frac{3\pi}{2} \]
Therefore, the value of \( c \) is \( -\frac{3\pi}{2} \).
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Simplify this solution Mind Expander
To find the value of \( c \) that shifts the graph of \( \sin x \) to the left by \( \frac{3\pi}{2} \) units, we use the property that \( \sin(x+c) \) is shifted to the left when \( c \) is negative. A shift of \( \frac{3\pi}{2} \) to the left can be represented as \( c = -\frac{3\pi}{2} \). Thus, the value of \( c \) is \( c = -\frac{3\pi}{2} \).
