Question

10 trigonometric ratios and functions exam
write the equation of a trigonometric function for the sinusoid shown.
a) y = 2 cos x
b) y = 2 cos x - 1
c) y = 2 sin x + 1
d) y = 2 sin x - 1

Explanation:

Step1: Check the amplitude

The amplitude $A$ of a sinusoidal function $y = A\sin(x)+k$ or $y=A\cos(x) + k$ is half of the vertical distance between the maximum and minimum values. The maximum value of the given curve is $2$ and the minimum is $- 2$. So, $A=\frac{2 - (-2)}{2}=2$.

Step2: Check the y - intercept

For $y = 2\cos(x)$, when $x = 0$, $y=2\cos(0)=2$. For $y = 2\cos(x)-1$, when $x = 0$, $y=2\cos(0)-1=2 - 1=1$. For $y=2\sin(x)+1$, when $x = 0$, $y=2\sin(0)+1=1$. For $y = 2\sin(x)-1$, when $x = 0$, $y=2\sin(0)-1=-1$. The given sinusoid has a $y$-intercept of $2$. The general form of a cosine function is $y = A\cos(x)+k$. With $A = 2$ and $k = 0$ (since there is no vertical shift for $y = 2\cos(x)$ as the mid - line is $y = 0$), the function is $y=2\cos(x)$.

Answer:

A. $y = 2\cos x$