Unit Circle Video Index

Video INDEX with DETAILs

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Introduction

(00:01) Welcome to the circle
(00:27) ♪ music by Louise Goffin: Sometimes a circle feels like a direction
(00:43) ♪ music by Louise Goffin: This noise in my head. Some things are easier done than said

Point, Axes

(01:08) Your point at origin
(01:18) X and Y axes
(01:33) your point becomes a Stickman
(01:42) axes range -5 to +5

XY Coordinate System

(01:57) Coordinate, address of a point
(02:00) pair of values
(02:04) x-coordinate
(02:12) y-coordinate
(02:27) coordinate (0,0)
(02:41) sunshine
(02:47) coordinate (1,0)
(03:04) coordinate (2,0)
(03:19) coordinate (-1,0)
(03:40) steps to the sun
(04:16) coordinate (2,3)
(04:40) ♪ music by Louise Goffin: Up and down, still lookin' for perfection
(04:50) arabesque
(04:59) Wind
(05:03) bounce down
(05:07) Rain
(05:22) land in Water
(05:31) Rainbow
(05:33) pot of gold

Quadrants

(05:39) NE Quadrant, I
(05:52) NW Quadrant, II
(06:01) SW Quadrant, III
(06:10) SE Quadrant, IV

Draw a Circle

(06:19) Point
(06:24) Line to another Point
(06:30) Circle from points of same distance
(06:39) Circle definition
(06:48) Perimeter
(07:03) Flatten the circumference into into a straight line
(07:20) Radius
(07:36) Diameter

Where did Pi come from?

(08:19) C = pi d
(08:26) ratio of circumference to diameter
(08:40) Pi is about 3.14
(08:51) Pi with 5 decimal places is 3.14159
(08:58) Pi with 15 decimal places is 3.141592653589793
(09:14) pattern for equation to calculate Pi
(09:54) approximate Pi with 22/7 to 2 decimal places
(10:06) approximate Pi with 355/113 to 6 decimal places
(10:37) Pi is the greek letter for 'p'
(10:48) area inside a circle is pi r^2
(10:53) ♪ music by Louise Goffin: Sometimes a circle feels like a direction

Circumference, Diameter, Radius

(10:56) back to a point
(11:00) C is circumference
(11:22) radius is half the diameter, diameter is twice the radius
(11:32) substitute 2r for d
(11:46) Constants
(11:57) Variables
(12:13) C=2 pi r

Angles, Degrees, Radians

(12:31) Circle is 360°
(12:35) Circle is 2pi radians
(12:44) divide 360° by 2pi
(12:49) a radian is about 57.3°
(13:01) a circle never ends
(13:19) Half a circle, 180°, pi
(13:47) Fourth of a circle, 90°, pi/2
(14:01) Three quarters of a circle, 270°, 3pi/2
(14:16) 45°, pi/4 (eight of a circle)
(14:37) 135°, 3/4 pi
(14:59) label Pi angles to be over 4
(15:30) 225°, 5pi/4
(15:57) 315°, 7pi/4

Temperature Degrees

(16:24) Temperature is also measured in degrees, but they aren't related to circles

45° Radius

(16:43) Focus on radius at pi/4, or 45°
(16:48) y-coordinate is height of Y
(17:07) x-coordinate is width of X
(17:19) Right triangle
(17:44) little square at right angle

Pythagorean Theorem

(17:52) Pythagoras
(18:06) Pythagorean theorem for right triangles
(18:39) Pythagorean theorem for circles
(18:59) solve to determine the actual values of x and y
(19:08) write 'knowns'
(19:19) x=y
(19:23) r=1
(19:41) make substitutions
(19:44) x^2 + y^2 = 1
(20:14) x^2 + x^2 = 1
(20:21) 2x^2 = 1
(20:28) x^2 = 1/2
(20:35) x=SquareRoot(1/2)
(20:48) x=SquareRoot(0.5)
(21:02) estimate
(21:05) 7x7 = 49
(21:09) 0.7x0.7 = 0.49
(21:32) x = 0.707
(21:36) y = 0.707
(21:47) Unit Circle from -1 to 1
(22:14) grid with distances

Trigonometry

(22:27) side lengths and angles of triangles
(22:37) tri = 3 in Greek
(22:40) trigonon = 3 angles in Greek
(22:44) metron = measure in Greek
(22:57) Greek letter 'theta' represents angle
(23:08) Sine
(23:27) Cosine
(23:41) Tangent

Angle, Sine, Cosine, Tangent

(24:00) make a table for angle, sine, cosine, and tangent
(24:16) sine, cosine, tangent for angle = 0°
(24:48) sine, cosine, tangent for angle = 45°
(25:36) sine, cosine, tangent for angle = 90°
(25:52) undefined because you can't divide by 0
(26:08) sine, cosine, tangent for angle = 135°
(27:09) sine, cosine, tangent for angle = 180°
(27:40) sine, cosine, tangent for angle = 225°
(28:12) positive slope is SW to NE
(28:31) sine, cosine, tangent for angle = 270°
(28:56) sine, cosine, tangent for angle = 315°
(29:38) negative slope is NW to SE
(29:45) sine, cosine, tangent for angle = 360°
(29:58) slope of 0 means y doesn't change as x changes
(30:11) charts to lookup sine, cosine, and tangent for any angle
(30:21) design view of Access Query to show Angle, Sine, Cosine, and Tangent

Inverse Trigonometric Functions

(30:38) calculate angle in radians
(30:41) ArcTangent
(30:53) ArcCosine
(31:02) ArcSine

Height of Tree

(31:36) wonder how tall a tree is?
(31:47) triangles with same angles have same ratios between side lengths
(32:08) x1 is the horizontal distance to the pole
(32:12) x2 is the horizontal distance to the tree
(32:16) y is the height to your eyeballs
(32:22) y1 is the vertical height between eyeball height and pole height
(32:31) y2 is what we want to figure out
(32:39) ratio between y2 and x2 is same as ratio between y1 and x1
(32:48) y2 = y1/x1 times x2
(32:55) height of tree = y2 + y

Applications for Trigonometry

(33:04) partial list of topics trigonometry can be used for

Summary

(34:15) brief summary

Why did I make this video?

(34:39) teach how to calculate point coordinates for analog clock
(34:51) calculate XY coordinates of any point
(35:07) drew graphics with Access
(35:19) Access is a database management application
(35:25) if you can imagine it, and simplify it, Access can do it

Music ♪ by Louise Goffin

(35:30) Thanks for the music ♫

Teachers

(36:24) show Unit Circle video to your class. my email address.
(36:31) free download
(36:34) test questions

Do you need help? Math tutoring, Access training & development

(36:39) contact me
(36:41) math tutor
(36:45) Access developer
(36:47) msAccessGurus.com
(36:51) ♪ Music by Louise Goffin, 'Sometimes a Circle'

Through sharing, we'll all get better

(36:58) Thanks for joining me.

Time-coded Index for Unit Circle Video

Concepts

Teachers

Video INDEX with DETAILs

Introduction

Point, Axes

XY Coordinate System

Quadrants

Draw a Circle

Where did Pi come from?

Circumference, Diameter, Radius

Angles, Degrees, Radians

Temperature Degrees

45° Radius

Pythagorean Theorem

Trigonometry

Angle, Sine, Cosine, Tangent

Inverse Trigonometric Functions

Height of Tree

Applications for Trigonometry

Summary

Why did I make this video?

Music ♪ by Louise Goffin

Teachers

Do you need help? Math tutoring, Access training & development

Through sharing, we'll all get better

Share

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