Graph r=1+cos(x)

Math
r=1+cos(x)
Rewrite the expression as cos(x)+1.
cos(x)+1
Use the form acos(bx-c)+d to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a=1
b=1
c=0
d=1
Find the amplitude |a|.
Amplitude: 1
Find the period using the formula 2π|b|.
Tap for more steps…
The period of the function can be calculated using 2π|b|.
Period: 2π|b|
Replace b with 1 in the formula for period.
Period: 2π|1|
Solve the equation.
Tap for more steps…
The absolute value is the distance between a number and zero. The distance between 0 and 1 is 1.
Period: 2π1
Divide 2π by 1.
Period: 2π
Period: 2π
Period: 2π
Find the phase shift using the formula cb.
Tap for more steps…
The phase shift of the function can be calculated from cb.
Phase Shift: cb
Replace the values of c and b in the equation for phase shift.
Phase Shift: 01
Divide 0 by 1.
Phase Shift: 0
Phase Shift: 0
Find the vertical shift d.
Vertical Shift: 1
List the properties of the trigonometric function.
Amplitude: 1
Period: 2π
Phase Shift: 0 (0 to the right)
Vertical Shift: 1
Select a few points to graph.
Tap for more steps…
Find the point at x=0.
Tap for more steps…
Replace the variable x with 0 in the expression.
f(0)=1+cos(0)
Simplify the result.
Tap for more steps…
The exact value of cos(0) is 1.
f(0)=1+1
Add 1 and 1.
f(0)=2
The final answer is 2.
2
2
2
Find the point at x=π2.
Tap for more steps…
Replace the variable x with π2 in the expression.
f(π2)=1+cos(π2)
Simplify the result.
Tap for more steps…
The exact value of cos(π2) is 0.
f(π2)=1+0
Add 1 and 0.
f(π2)=1
The final answer is 1.
1
1
1
Find the point at x=π.
Tap for more steps…
Replace the variable x with π in the expression.
f(π)=1+cos(π)
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
f(π)=1-cos(0)
The exact value of cos(0) is 1.
f(π)=1-1⋅1
Multiply -1 by 1.
f(π)=1-1
f(π)=1-1
Subtract 1 from 1.
f(π)=0
The final answer is 0.
0
0
0
Find the point at x=3π2.
Tap for more steps…
Replace the variable x with 3π2 in the expression.
f(3π2)=1+cos(3π2)
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
f(3π2)=1+cos(π2)
The exact value of cos(π2) is 0.
f(3π2)=1+0
f(3π2)=1+0
Add 1 and 0.
f(3π2)=1
The final answer is 1.
1
1
1
Find the point at x=2π.
Tap for more steps…
Replace the variable x with 2π in the expression.
f(2π)=1+cos(2π)
Simplify the result.
Tap for more steps…
Simplify each term.
Tap for more steps…
2π is a full rotation so replace with 0.
f(2π)=1+cos(0)
The exact value of cos(0) is 1.
f(2π)=1+1
f(2π)=1+1
Add 1 and 1.
f(2π)=2
The final answer is 2.
2
2
2
List the points in a table.
xf(x)02π21π03π212π2
xf(x)02π21π03π212π2
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude: 1
Period: 2π
Phase Shift: 0 (0 to the right)
Vertical Shift: 1
xf(x)02π21π03π212π2
Graph r=1+cos(x)

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top