Description
Coordinates
How and Why?
Once you understand the logic,
learning angles and coordinates isn't memorizing with no reason.
After figuring out why it works, for yourself,
it can be good, however, to memorize basic values.
Start with a point, create a coordinate system. Add axes for reference, and a grid to see values easier. Mark coordinates as you move around as a stickman on your adventures in the sun to the wind and rain, and into a pond. Leigh Ann, I thought about you when stickman was doing an arabesque on top of steps! The day brightens as the sun comes out and makes a rainbow ending in a pot of gold. Left and right, up and down, positive and negative values, the four quadrants.
From your point, extend a line to another point. Mark more points the same distance away to draw a circle. Flatten the circle into a straight line so you can measure it.
Where did Pi come from? Discover that Pi is the ratio between circumference and diameter. Learn how to calculate and approximate it, and why its called 'pi'. Constants, variables, C=pi*d
See how 360° is 2 pi radians ... and temperature degrees aren't the same at all. Move around the circle in 90° increments to label angles in degrees and radians. Then fill in 45° increments.
Pythagorean Theorem
Use the Pythagorean theorem for a right triangle, a^2+b^2=c^2,
to calculate x and y when the angle is 45°.
Write 'knowns' and make substitutions to isolate and solve for x.
Calculate that x and y are both about 0.707
and then observe that is true.
0.717 is half the square root of 2 (1.414),
and good value to memorize.
Trigonometry, Angle, Sine, Cosine, Tangent
What is Trigonometry? How Sine and Cosine relate to the y- and x-coordinates. Make a table with Angle, Sine, Cosine, and Tangent. Calculate or observe values for each point corresponding to angles in increments of pi/4, or 45°. See how tangent correlates to slope of the radius. Inverse trignometric functions.
How can knowing about trigonometry help you? Wonder how tall a tree is? There's an easy way to figure it out. Learn how!
Do you want to build?
make those shots in pool?
figure out locations before or after something happens or happened?
Teachers
Teachers ... email me.
I will freely send test questions,
and a download link for the video if you don't have a connection in the training room.
If you simply have a television and DVD player,
a DVD disc can be made.
Drawings illustrate concepts.
Terms are defined.
It is my hope that, after watching this lesson,
these ideas will be easier to remember.
