By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the xaxis and write linear equations in standard form as evidenced by a mixmatch activity ID: 675260
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Slide1
7.6 Normal Form of a Linear Equation
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.Slide2
What is a “Normal” Line
We find an equation of a line using a point and a slope
Distance between two points comes from the Pythagorean theorem
Slope can be found using “Normal” mean perpendicularPerpendicular slopes are OPPOSITE sign and RECIPROCAL
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.Slide3
Sides of a Triangle
- Greek letter can be pronounced either fee (as in a bank fee) or fi (rhymes with pie)Thus, the sides of our triangle can be found using the angle and the length of the hypotenuse
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
Slide4
What is a “Normal” Line
is the
distance
between the origin and the line(distance is measured PERPENDICULARLY) is the angle made with the positive x-axis By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
We want the equation of THIS lineSlide5
What is a “Normal” Line
How do we get the normal line?
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
We want the equation of THIS lineSlide6
How is Normal Form Different than Standard form?
Normal
Standard
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
Why do you have a problem with the last bullet points?
What is the difference between Normal and Standard?
Ratio coefficients
Positive leading
coeff
.
Non ratio coefficientsSlide7
By the end of the section students will be able
to write
the standard form
of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.Example 1: Write the normal form of the equation given by the length of the normal segment and the angle made with the positive x axis
Slide8
By the end of the section students will be able
to write
the standard form
of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.Example 1: Write the normal form of the equation given by the length of the normal segment and the angle made with the positive x axis
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
Slide9
How do we convert from standard form to normal
form?
Normal
Standard
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
Divide everything by
,
use the opposite sign of the value for
C
This is a sin value
This is a
cos
value
Opposite, y
Hypotenuse, p
adjacent, x
Slide10
Where are all the angles??
Which quadrant is being described by each?
What is the measure of an angle?
Values like are found on the unit circle, we can give EXACT angles
Ratios that we don’t recognize can still be found using
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.Slide11
Example 2: Write the standard form of the equation and identify
and
given the normal form
What do we divide by? How do we know which sign to use? opposite of C
??? WHAT??? This is not in quadrant 3??
The calculator gives you the PRINCIPAL value, you need to translate that to the appropriate quadrant
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
are not fractions
For the HW this is acceptable, UNLESS it’s a unit circle
value
What quadrant is this angle in
?
By the end of the section students will be able to
write the standard form of a linear equation
given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
Slide12
What quadrant is this angle in
?
If you can identify the angle at this step from sin and cos, you may do so.Example 2: Write the standard form of the equation and identify and given the normal form
What do we divide by?
How do we know which sign to use?
opposite of
C
Which of these will give use the quadrant we want?
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
are not fractions
For the HW this is acceptable, UNLESS it’s a unit circle
value
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
Slide13
Example 2: Write the standard form of the equation and identify
and
given the normal form
What do we divide by? How do we know which sign to use? opposite of C
This angle is in quadrant 4 so
What if our angle was in quadrant 2?
Use
as the reference angle for QII
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
are not fractions
For the HW this is acceptable, UNLESS it’s a unit circle
value
What quadrant is this angle in
?
By the end of the section students will be able to
write the standard form of a linear equation
given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
Slide14
Example 2: Write the standard form of the equation and identify
and
given the normal form
What do we divide by?
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
are not fractions
Slide15
Example 2: Write the standard form of the equation and identify
and
given the normal form
What do we divide by? How do we know which sign to use? opposite of C +
Which of these will give use the quadrant we want?
By the end of the section students will be able to
write the standard form of a linear equation
given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.
are not fractions
What quadrant is this angle in
?
For the HW this is acceptable, UNLESS it’s a unit circle
value
Slide16
Summary
Write the equation
in normal form.
Write the standard form of the equation of a line for which the length of the normal is and makes and angle of with the positive . By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.Slide17
Summary
Write the equation
in normal form
.
Write the standard form of the equation of a line for which the length of the normal is
and makes and angle of
with the positive
.
By the end of the section students will be able to write the standard form of a linear equation given the length of the normal and the angle it makes with the x-axis and write linear equations in standard form as evidenced by a mix-match activity.