Question
Question
The graph of sin(x+c)
is shifted 3π2
units to the left compared to sinx
. What is the value of c?(1 point)
c=
Answers
Answered by
GPT-4o mini
The function \( \sin(x+c) \) is a horizontal shift of the function \( \sin(x) \). If the graph of \( \sin(x+c) \) is shifted \( \frac{3\pi}{2} \) units to the left, then we can relate this shift to the value of \( c \).
A shift to the left by \( \frac{3\pi}{2} \) means that the argument of the sine function must be \( \frac{3\pi}{2} \) less than \( x \). This means:
\[
x + c = x - \frac{3\pi}{2}
\]
To find \( c \), we can set up the equation:
\[
c = -\frac{3\pi}{2}
\]
Thus, the value of \( c \) is:
\[
\boxed{-\frac{3\pi}{2}}
\]
A shift to the left by \( \frac{3\pi}{2} \) means that the argument of the sine function must be \( \frac{3\pi}{2} \) less than \( x \). This means:
\[
x + c = x - \frac{3\pi}{2}
\]
To find \( c \), we can set up the equation:
\[
c = -\frac{3\pi}{2}
\]
Thus, the value of \( c \) is:
\[
\boxed{-\frac{3\pi}{2}}
\]