what are the horizontal and vertical intercepts :r=4-4cos(theta) please show work
x=-9 x=0
y-4
y=0
y=-4
You will run horizonally if θ is zero or θ = 180°
so r = 4 - 4cos0 = 0 , which corresponds to (0,0) in cartesian coordinates
or r = 4 - 4cos180 = 8 , which corresponds to (-8,0)
to run vertically θ = 90 or θ = 270
if θ=90° , r = 4 - 4cos90 = 4 , which corresponds to (0,4)
if θ = 270, r = 4 - 0 = 4, which corresponds to (0,-4)
check: https://www.wolframalpha.com/input/?i=polar+plot+r%3D4-4cos%CE%B8
To find the horizontal and vertical intercepts of the equation r = 4 - 4cos(theta), we need to substitute specific values for theta and solve for r.
To find the horizontal intercept, we set r = 0 and solve for theta.
0 = 4 - 4cos(theta)
Rearranging the equation, we have:
4cos(theta) = 4
Dividing both sides by 4:
cos(theta) = 1
This means that theta = 0° (or 360°) because the cosine of 0° is equal to 1.
Therefore, the horizontal intercept occurs when theta is 0° or 360°.
To find the vertical intercept, we set theta = 90° (or any other multiple of 90°) and solve for r.
Setting theta = 90° in the equation:
r = 4 - 4cos(90°)
Since the cosine of 90° is equal to 0, the equation becomes:
r = 4 - 4(0)
r = 4
Therefore, the vertical intercept occurs when r is equal to 4.
In conclusion, the horizontal intercepts occur when theta is 0° and 360°, and the vertical intercept occurs when r is equal to 4.