Precalculus (6th Edition) Blitzer

The amplitude of $y=-4\cos \frac{\pi }{2}x$ is 4 and the period of $y=-4\cos \frac{\pi }{2}x$ is 4.
Consider the given equation, $y=-4\cos \frac{\pi }{2}x$ The equation is of the form $y=A\cos Bx$ with $A=-4$ and $B=\frac{\pi }{2}$. Amplitude of $y=-4\cos \frac{\pi }{2}x$ is given by $\left| A \right|=\left| -4 \right|=4$ Period of $y=-4\cos \frac{\pi }{2}x$ is given by $\frac{2\pi }{B}=\frac{2\pi }{\frac{\pi }{2}}=2\pi \times \frac{2}{\pi }=4$ Thus, the amplitude of $y=-4\cos \frac{\pi }{2}x$ is 4 and the period of $y=-4\cos \frac{\pi }{2}x$ is 4. Graph: Step1: Identify the amplitude and the period of $y=-4\cos \frac{\pi }{2}x$. The amplitude of $y=-4\cos \frac{\pi }{2}x$ is 4 means that the maximum value of $y$ is 4 and the minimum is $-4$. The period of $y=-4\cos \frac{\pi }{2}x$ is 4 means that each cycle is of length of 4. Step 2: Find the values of $x$ for the first five key points. Begin by dividing the period 4, by 4. $\frac{\text{period}}{4}=\frac{4}{4}=1$ Start with the value of $x$ where the cycle begins, ${{x}_{1}}=0$. Adding quarter periods 1, the five key points are: \begin{align} & {{x}_{1}}=0 \\ & {{x}_{2}}=0+1=1 \\ & {{x}_{3}}=1+1=2 \\ & {{x}_{4}}=2+1=3 \\ & {{x}_{5}}=3+1=4 \\ \end{align}