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9.4 POLAR FORM OF A LINEAR EQUATIONBy the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
Recall• NORMAL form of a linear equation
• Standard form
• Normal form with NO fractions or negative x coefficient
• To convert from standard to normal, divide by , choosing the sign OPPOSITE to C.
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
x
y
A
B
M
C
O
p
𝜙
𝜙
𝜙
𝑥+√3 𝑦−30=0
12𝑥+ √3
2𝑦−15=0
𝑥+√3 𝑦−30=0
√12+(√3 )2=212𝑥+ √3
2𝑦−15=0
This is the HYPOTENUSE of the triangle whose sides are A and B
Polar Form of a Linear Equation
Identify what changed in each step
The formula will be given to you.
• is a VARIABLE• is a VARIABLE• and are constants
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
x
y
A
B
M
C
O
p
𝜙
𝜙
𝜙
(𝑟 ,𝜃 )
𝜃
Example 1: Write the rectangular equation in polar formA. • To write the polar form we need to identify
and . • Our first step is to rewrite the STANDARD
form into NORMAL form.
divide by :
• What angle has a and ?
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
2
−1
−√360 °
𝜙=240 °
15=𝑟 cos (𝜃−240 ° )𝑝=𝑟 cos (𝜃−𝜙 )
Example 1: Write the rectangular equation in polar formB.
C.
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
2
−√2√2 45 °
𝜙=135 °
1
1√245 °
𝜙=45 °
Example 1: Write the rectangular equation in polar formD.
E.
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
2−1
√330 °
𝜙=330 °
2
−1
−√360 °
𝜙=240 °
Example 2: Write the rectangular (standard) form of the polar equationA.
What do we need for rectangular form?
and
Plug in
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
2 √2√245 °
Example 2: Write the rectangular form of the polar equationB.
C.
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
2
−1
√3 60 °
2−1
−√330 °
Example 2: Write the rectangular form of the polar equationD.
E.
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
2
1
−√360 °
2
√2−√2
45 °
Summary
1. Write the equation in polar form:
2. Write the equation in rectangular form:
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
Summary
1. Write the equation in polar form: Hypotenuse:
2. Write the equation in rectangular form:
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
21
−√330 °
2 √3
160 °
By the end of the section students will be able to write the polar form of a linear equation, and write the linear form of a polar equation as evidenced by an exit slip.
