The table represents a trigonometric function. Graph and identify the key features

Question

x.      0    Pi/4.    Pi/2     5Pi/6.   Pi.   4pi/3.    3pi/2.    11pi/6.     2pi

 

f(x). 0. (square root)2   2   1.   0.    -(square root)3    -2  -1      0

 

graph:

 

 

 

 

 

 

 

amplitude: 

period: 

midline

domain:

range:

even, odd or neither:

Answer 1

Hi Alicia.

 

The values look very similar to f(x) = sin(x).

 

sin(0) = 0

sin(pi/4) = sqrt(2)/2

sin(pi/2) = 1

sin(5pi/6) = 1/2

sin(pi) = 0

sin(4pi/3) = -sqrt(3)/2

sin(3pi/2) = -1

sin(11pi/6) = -1/2

sin(2pi) = 0

 

The only difference is that everything in the f(x) column of your table is doubled.

 

So, your function is:

 

f(x) = 2*sin(x)

 

For a general trig function:

 

f(x) = A*sin(Bx - C) + D

 

Amplitude = A

Period = 2pi/B

Phase Shift = C/B

Vertical Shift = D

 

In your case:

 

A = 2, B = 1, C = 0, D = 0

 

So your amplitude is 2.

 

Your period is 2pi/1 = 2pi

 

Your midline will be y = 0 since there's no vertical shift.

 

The domain of sine is unrestricted. It's All Real Numbers.

 

The range of sine is restricted to (A + D) and (-A + D). In your case, the range is -2 to 2.

 

Sine is an odd function, since sin(-x) = -sin(x).

 

Hope this helps.