which function is graphed below?\n\nf(x)=-cos(x)\nf(x)=cos(x)\nf(x)=sin(x)
which function is graphed below?\n\nf(x)=-cos(x)\nf(x)=cos(x)\nf(x)=sin(x)
Answer
Answer:
C. $f(x)=\sin(x)$
Explanation:
Step1: Recall cosine - sine properties
The cosine function $y = \cos(x)$ has a value of $1$ at $x = 0$, i.e., $\cos(0)=1$. The function $y=-\cos(x)$ has a value of $- 1$ at $x = 0$, i.e., $-\cos(0)=-1$.
Step2: Evaluate at $x = 0$ for the given graph
The graph has a $y$-value of $0$ at $x = 0$.
Step3: Recall the sine - function value at $x = 0$
The sine function $y=\sin(x)$ has $\sin(0)=0$. And its general shape (starting at the origin, having a maximum of $1$ at $x=\frac{\pi}{2}$, a minimum of $-1$ at $x = \frac{3\pi}{2}$) matches the given graph.