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.
Recallβ’ NORMAL form of a linear equation
β’ Standard form
β’ Normal form with NO fractions or negative x coefficient
β’ 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
π
π
π
π₯+β3 π¦β30=0
12π₯+ β3
2π¦β15=0
π₯+β3 π¦β30=0
β12+(β3 )2=212π₯+ β3
2π¦β15=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.
β’ is a VARIABLEβ’ is a VARIABLEβ’ 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
π
π
π
(π ,π )
π
Example 1: Write the rectangular equation in polar formA. β’ To write the polar form we need to identify
and . β’ Our first step is to rewrite the STANDARD
form into NORMAL form.
divide by :
β’ 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
β1
ββ360 Β°
π=240 Β°
15=π cos (πβ240 Β° )π=π cos (πβπ )
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
ββ2β2 45 Β°
π=135 Β°
1
1β245 Β°
π=45 Β°
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.
2β1
β330 Β°
π=330 Β°
2
β1
ββ360 Β°
π=240 Β°
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 β2β245 Β°
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
β1
β3 60 Β°
2β1
ββ330 Β°
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
ββ360 Β°
2
β2ββ2
45 Β°
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
ββ330 Β°
2 β3
160 Β°
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.