Question

Write the equation of the trigonometric graphs.

Answer 1

Answer:

$2 \cos(4x)$

Step-by-step explanation:

The highest and lowest value is 2 and -2 respectively so the amplitude is 2.

That also means the vertical translation is 0.

The graph is reaches it max every pi/2 units so the period is

pi/2.

Since the graph intersects a non zero value at 0, it will be the cosine function.

Step 2: A cosine function is

$a \cos(b(x - c)) + d$

where a is the amplitude

$\frac{2\pi}{ |b| }$

is the period

C is the horinzontal shift

d is the vertical shift

We know a is 2

D is 0.

To find b,

$\frac{2\pi}{b} = \frac{\pi}{2}$

$b = 4$

So as of right now we have

$2 \cos(4x)$