NEED ANSWERED ASAP Graph the following Trigonometric Function

Question

f(x)= -cos[1/2(x-5π/6)] on the interval [0,2π]

State:
amplitude
period
phase shift

equation of axis

domain

range

 

 

What is the mapping rule and the points on the graph?

Answer 1

The amplitude is the maximum distance from the x-axis the function occurs in which is the absolute value of the constant multiplied by the periodic function.

amplitude=|-1|=1

1/2*T=2π Thus, the period is T=4π

 

The phase shift is simply how much the the function is shifted towards the right or left on the x-axis, the constant angle being 5π/6 indicates the phase shift. The function is shifted 5π/6 to the right on the x-axis.

 

The equation of the axis is simply y=0 in which is the horizontal line in which the maximum value and minimum value of the function are equal distance from this common line.

 

The domain is [0,2π]

 

To range is [-1,1]. These are the values in which the function fluctuates. 

Answer 2

Please reference the other cosine problem for the explanation.

 

f(x)= -cos[1/2(x-5π/6)] on the interval [0,2π]

 

amplitude: |-1| = 1

 

period: 2π/(1/2) = 4π

 

phase shift: 5π/6

 

equation of axis: y = 0

 

domain: [0, 2π]

 

range: [-1,1]