Question Type 1: From graphs of trigonometric functions, finding the amplitude and period of the trigonometric curves Exercises

The graph of $y=k(x)$ oscillates between $-7$ and $1$, and one cycle spans $8$ units on the $x$-axis. What are the amplitude and period?

Find the amplitude and the period of the function.

A sine wave, defined for $x \ge 0$, has its first minimum at $x=2$ and its next minimum at $x=8$. The difference between the maximum and minimum values is $12$. Determine the amplitude and period.

A cosine curve passes through $(0, -3)$, reaches a maximum of $3$ at $x=\frac{\pi}{2}$, then next returns to $-3$ at $x=\pi$. Find the amplitude and period.

Consider the function $f(x) = 3 \cos(2x)$.

Write down the amplitude and period of $f(x)$.

A sine curve has consecutive peaks at $x=1$ and $x=4$. The maximum value is $6$ and the minimum is $2$. Determine the amplitude and period.

The graph of $y=g(x)$ oscillates between $-2$ and $2$, completing three full cycles over the interval $[0, 6\pi]$. Find the amplitude and period.

A sine curve reaches its maximum of $5$ at $x = \frac{\pi}{6}$ and its next minimum of $-5$ at $x = \frac{5\pi}{6}$. Determine the amplitude and period of this curve.

The function $y=h(x)$ has equation $y=4\sin\bigl(5x\bigr)$. Without graphing, state its amplitude and period.