Graph y=cos(x/2-pi/4)

Problem

y=cos(x/2−π/4)

Solution

1. Identify the general form of the trigonometric function, which is y=A*cos(B*(x−C))+D

2. Factor out the coefficient of x to find the phase shift.

y=cos(1/2*(x−π/2))

3. Determine the amplitude A The coefficient of the cosine function is 1

|A|=1

4. Calculate the period P using the formula P=(2*π)/B where B=1/2

P=(2*π)/(1/2)=4*π

5. Identify the phase shift C The value inside the parentheses indicates a shift to the right.

C=π/2

6. Find the vertical shift D There is no constant added to the function.

D=0

7. Determine the key points for one cycle by dividing the period into four equal parts of π Starting at the phase shift x=π/2

(x_1)=π/2⇒y=1

(x_2)=(3*π)/2⇒y=0

(x_3)=(5*π)/2⇒y=−1

(x_4)=(7*π)/2⇒y=0

(x_5)=(9*π)/2⇒y=1

Final Answer

y=cos(x/2−π/4)* has amplitude *1, period *4*π, and phase shift π/2

Want more problems? Check here!