Question

write the equation for the trigonometric function based on its graph. (1 point) \\(\bigcirc\\) \\(y = \sin(x) - 2\\) \\(\bigcirc\\) \\(y = \sin(x) - 4\\) \\(\bigcirc\\) \\(y = \cos(x) - 3\\) \\(\bigcirc\\) \\(y = \sin(x) - 3\\)

Explanation:

Step1: Recall the general form of a trigonometric function

The general form of a sine function is \(y = A\sin(Bx - C)+D\) and for a cosine function \(y = A\cos(Bx - C)+D\). Here \(A\) is the amplitude, \(B\) affects the period (\(T=\frac{2\pi}{|B|}\)), \(C\) is the phase - shift (\(\text{Phase shift}=\frac{C}{B}\)), and \(D\) is the vertical shift.

Step2: Check the vertical shift

When \(x = 0\):

• For \(y=\sin(x)-2\), \(y=\sin(0)-2=- 2\)
• For \(y=\sin(x)-4\), \(y=\sin(0)-4=-4\)
• For \(y=\cos(x)-3\), \(y=\cos(0)-3=1 - 3=-2\)
• For \(y=\sin(x)-3\), \(y=\sin(0)-3=-3\)

The graph passes through the point \((0,-3)\).

Answer:

\(y=\sin(x)-3\)