Download Appendices B & D: A Quick Review of Some

Appendices B & D: A
Quick Review of
Some Fundamentals
Friday, August 27, 2004
Coordinate Geometry


Rectangular/Cartesian Coordinates (x,y)
Distance Formula
P1P2  ( x2  x1 )  ( y2  y1 )
2
2
Slope
y y2  y1
m

x x2  x1
Slope of a vertical line is undefined
Equation of a Line
An equation of the line passing through t he point
P1 (x1 , y1 ) and having slope m is
y  y1  m( x  x1 )
An equation of the line with slope m
and y - intercept b is
y  mx  b
General Form
The equation of every line can be written
in the form Ax + By + C = 0
 Slope is –A/B
 Y-intercept is –C/B

Parallel and Perpendicular Lines
Two non-vertical lines are parallel if they
have the same slope
 Two lines with slopes m1 and m2 are
perpendicular if and only if m1m2=-1
(slopes are negative reciprocals)

Example

Find an equation of the line through the
point (3,2) that is parallel to the line 4x +
5y + 6 = 0
Trigonometry review
How many degrees in π radians?
 How many radians in 30°?

Radius and Arc Length

If the radius of a circle is 5cm, what angle is
subtended by an arc of 6 cm?
a  r

Remember the equation is only valid when θ is
measured in radians.
Trig Functions
Review trig functions on page A26 of text
 Find the exact trigonometric ratios for
θ=2π/3

Trigonometric Identities
Page A28 of Text
 Also found on Reference Card

Some Problems

Prove the following trigonometric identity
(sin x  cos x)  1  sin 2 x
2
Another One
sin 3  sin   2 sin 2 cos
Some Homework

Page A32-33: 13, 30, 36, 60, 65, 69, 70,
76