Question

graph the polar equation 2 = r cos(theta– 20°)

Answer 1

we are using degrees here

Answer 2

yes i think

Answer 3

one way to do it, which is fast, is to use a graphing calculator.
another way is to make a table

Answer 4

i can find my graphing calculator;/

Answer 5

we can also expand the right side using angle difference formula

Answer 6

$$ \Large \cos(A-B) = \cos A \cos B + \sin A \sin B $$

Answer 7

cos (a-b)=2b

Answer 8

$$ \Large \cos(\theta -20~^o) = \cos \theta \cos 20^o + \sin \theta \sin 20^o $$

Answer 9

$$ \Large{
2 = r \cos(\theta -20~^o)\\
\\ \iff \\
2 = r[ \cos \theta \cos 20^o + \sin \theta \sin 20^o ]
\\ \iff \\
2 = r \cos \theta \cos 20^o + r\sin \theta \sin 20^o
\\ \iff \\
2 = \color{red}x \cos 20^o + \color{red}y \sin 20^o


}$$

Answer 10

thats an equation of a line

Answer 11

so a

Answer 12

we can simplify that further

Answer 13

ow got it

Answer 14

$$ \Large{
2 = r \cos(\theta -20~^o)\\
\\ \iff \\
2 = r[ \cos \theta \cos 20^o + \sin \theta \sin 20^o ]
\\ \iff \\
2 = r \cos \theta \cos 20^o + r\sin \theta \sin 20^o
\\ \iff \\
2 = \color{red}x \cos 20^o + \color{red}y \sin 20^o
\\ \iff \\
y \sin 20^o = -x \cos 20^o + 2
\\ \iff \\
y = -x \cdot \frac{\cos 20^o}{\sin 20^o} + \frac{2}{\sin 20^o}

}$$

Answer 15

so we are looking for a line with a negative slope and a positive y intercept

Answer 16

an easier way to do this is to plug in angles into the original polar equation

Answer 17

start with theta = 0, and theta = 90

Answer 18

$$
\Large {
2 = r \cos(\theta -20~^o)\\
\\ \iff \\
r = \frac{2}{\cos(\theta -20~^o)\\}
\\ \therefore
r = \frac{2}{\cos(\color{red}{20^0} -20~^o)\\} = \frac{2}{\cos(0)}= 2 / 1 = 2

}

$$

Answer 19

so that narrows it down to a) , since at 20 degrees you have radius 2

Answer 20

thanks so much @perl