Graph the polar equation: 2=r cos(theta + 180)
2=r(costheta cos180+sintheta sin180)
2=r(1/2costheta +pi+ pi sintheta)
2=1/2rcostheta + pi rsintheta
2=1/2x+ pi y
4=x+ pi
0= x + pi-4
how do i graph?
trig identity is
cos (a+b) = cos a cos b - sin a sin b
I think you have the sign wrong.
use pi radians for 180 deg
let t = theta
2 = r (cos t cos pi - sin t sin pi)
cos pi = -1 and sin pi = 0
2 = r (- cos t)
r cos t = -2
x = -2
vertical line through x = -2
note y = r sin t
so y = (-2/cos t)sin t
y = -2 tan t
tan t takes all values from -oo to +oo as t goes from 0 to 2 pi. In other words the entire vertical line.
Thank you I understand now.
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To graph the given polar equation, 2 = r cos(theta + 180), you can follow the steps below:
1. Convert the polar equation into rectangular coordinates. Recall that x = r cos(theta) and y = r sin(theta). In this case, we have:
2 = r cos(theta + 180)
2 = r(cos(theta) cos(180) + sin(theta) sin(180))
2 = r(cos(theta) (-1) + sin(theta) (0))
2 = -r cos(theta)
2. Simplify the equation: Since -r cos(theta) is the same as -x, we can rewrite the equation as:
2 = -x
x = -2
3. Plot the graph: Draw a straight line passing through the point (-2, 0) on the x-axis. This line represents the graph of the equation x = -2. It is a vertical line touching the x-axis at x = -2.
That's it! You have successfully graphed the given polar equation.