Graph the polar equation: 2=r cos(theta + 180)

Question

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?

Answer 1

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.

Answer 2

Thank you I understand now.

Answer 3

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