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Fall 2022

    Precalc Notes

Functions, Vocabulary     Quadratic Functions Exponent & Log Laws
Orientation, ... Higher Order Polynomials Trig Functions, "Before Unit Circle"
Calculator Resources Rationals Trig Functions, "Unit Circle & On"
Lines Log & Exponential Functions     Trig Cheat Sheet


TAN GENTS AND OTHER THINGS OF INTEREST
-- vocabulary, spreadsheets, Sketchpads, graph papers, connect the dots, sine law and unit circle manipulatives
 
  Spring 2020 Trig Note Sheets and Connect-the-Dots
1., 2. pdf of circles, angles, degrees, radians, triangles, square
3., 4. pdf of 30-60-90 and 45-45-90 triangles and trig functions of
      30°, 60°, and 45° angles
5. gif of answers to 3. and 4. all functions of the 30s, 45s, and 60s
6. pdf of quiz 5.1 on trig functions
7. gif of quiz 5.1 gif file
8. gif of answers to quiz 5.1
9. pdf of Oscar Connect-the-Dots Questions
      find trig functions of angles in a right triangle
10. gif of answers to 9. Oscar Connect-the-Dots
11. pdf of Find sides and angles of geometric figures con-dots
12. gif of answers to con-dots 11
13. pdf of Veronica's Bow Tie &
      All Students Try Cheating Worksheet/Note Sheet
14. gif of answers to Veronica's Bow Tie ...
15. pdf of quadrantials notes
15. gif of quadrantials notes answers
16. pdf of fx all qradrants no triangles con-dots
17. gif of fx all qradrants no triangles con-dots answers
18. pdf of Unit Circle Notes
18. gif of Unit Circle Notes
19. gif of plane paper, 3 planes per page
19., 20. pdf of plane paper, 3 planes per page
      to graph sine, cosine, and tangent, then dash these
      on another sheet & graph their reciprocals
22. pdf of functions of angles on a plane con-dots
23. gif of answers to functions of angles on a plane con-dots
24. pdf of fx all quadrants w angles drawn con-dots
25. gif of answers to fx all quadrants w angles drawn 25 con-dots
26. pdf of Arcfunction Notes
26. gif of Arcfx Notes
27. pdf of use arcfx to solve triangles con-dots
27. gif of use arcfx to solve triangles con-dots
28. gif of answers to use arcfx to solve triangles 27 con-dots
29.-30.-31. 1-page pdf of 2 hour Trig "review" con-dots
32. 2-page pdf of 2 hour Trig "review" con-dots
29. 1-page gif of 2 hour Trig "review" con-dots
29. gif of 2 hour Trig "review" con-dots
30. gif of questions on the 2 hour Trig "review" con-dots
31. gif of array of answers dots on the Trig "review" con-dots
32. gif of connected answer dots on the Trig "review"
33. gif of first column text of answer on the Trig "review"
34. gif of second column text of answer on the "review"


Trig Functions, but Not the Unit Circle

Sides
opposite
adjacent
hypotenuse      
 
Right Triangle Sides & Angles --      
equilateral triangle
30-60-90 triangle
the square
45-45-90 triangle
 
Fractions, Radians, Angles            
- Radian Measure      
Race Track  
degree to radian
radian to degree
 
Degrees & Radians
90s       90s Answers
45s       45s Answers
60s       60s Answers
30s       30s Answers
 
Trig Functions of
Reference & Special Angles      
trig30s
trig45s
trig60s
trig90s
 
Veronica's Bow Tie
Questions
Answers
Quadrantal Q & A
Central Angles
In math
In physics
What's a Radian?
Sine, Cosine, Tangent
sine
cosine
tangent
trig tables - all functions
Arc Functions -- Inverse Trig Functions
Arc and arc functions web page
All Arc Functions Images
Ranges, Given Domain
arcsine
arccosine
arctangent

Trig Functions Including the Unit Circle

Trig Functions Summary Pages
Lessons 330 - Trig Functions
 
Graphing Trig Functions
blank 3-planes
sine-cosine-tangent graphed
cosecant-secant-cotangent graphed            
The Unit Circle
Animated Unit Circle Web Page
-- Text w/animation
Static Pictures
Black Unit Circle
Colored Unit Circle
Digital Manipulativeof the Unit Circle
See them below.
Puzzle
2 masters on a page.
See Digital Manipulative at this location.
 
 
Pythagorean Trig Identities
sine-cosine, sin2(A) + cos2(A) = 1
tangent-secant, tan2(A) + 1 = sec2(A)
cotangent-cosecant, cot2(A) + 1 = csc2(A)
 
Curve Shifting
Graph f(x) = Asin(Bx - C) + D
Graph
    f(x) = [Asin(Bx - C) + D] + [Asin(Bx - C) + D]
See Both Dynamic Spread Sheet below.
 
Triangle Solving
including Law of Sines, Law of Cosines
Dynamic Spread Sheet below.
 
Sine Law Ambiguous Case
Web page w/ pictures & text
manipulative masters
Digital Manipulative at this location.
Trig Summary
2 Hours of Trig Connect-the-Dots
· Simplify Trig Expressions,
· Simplify Arcfunction Expressions,
· Solve Equations,
· Spiced w/Identities & Function Properties
 
Cheat Sheets of Trig Identities
Pythagorean Identities, Cofunctions, Odd/Even Functions
Sine, Cosine, & Tangent of the Sums & Differences
Double & Half Angle Formulas
(Signs of the Trig Functions)
cheat.pdf including Veronica's Bow Tie
cheat of just 30-45-60 1st day
 
mathtokens.com home
Digital Manipulatives -- Dynamic Tokens
  • sinelaw.xls DIGITAL MANIPULATIVE
  • jig1.xls -- UNIT CIRCLE PUZZLE

spread sheet notes
Spread Sheets -- Dynamic Computation
    solvtrig.xls
    -- solve all sorts of triangles, Law of Sines, Law of Cosines
    sine.xls -- Asin(Bx-C)+D, sine, cosine, tangent, or sine & cosine

sketchpad
Sketch Pads -- Dynamic Analytic Geometry
    Right Triangle Trig
  • cosplay   -- just right triangle cosine
    • TraceSin   -- just graph with a slideable point to display coordinates
  • sinplay   -- just right triangle sine
  • tanplay   -- just right triangle cosine
    Unit Circle and Identities
  • unitSinCosTriangle   -- sine & cosine functions with a unit circle
  • unitTanSec   -- tangent & secant functions with a unit circle
  • unitCotCsc   -- cotangent & cosecant functions with a unit circle
  • unitfx   -- 6 functions with a unit circle
  • Pythagorean   -- using only figure to adjust angle
  • PythagorIdentities   -- using either figure or parameter theta to adjust angle
    Trig
  • 2TrigGraphs.gsp  -- 1 blank function, 1 parameter-driven
          function on a "trig plane"
  • SinCosTan1stDay   -- Just sine, cosine, tangent of right triangle angles.
  • SinCosTan6fx   -- All 6 functions in right triangle only.
  • SinCosTanAllNumbers   -- All 6 functions in right triangle and forall numbers,
        * controlled by figure for right triangle,
        * parameter-defined angle measure in degrees for all measures, and
        * parameter-defined angle measure in decimal number
          times pi for radian measures
  • sinNcos.gsp   -- sine and cosine in right triangle only
  • TraceCos   -- drag point f(x) to state and show new ( x, f(x))
  • TraceSin   -- drag point f(x) to state and show new ( x, f(x))
  • 2 Sine Functions -- Asin(Bx-C) + D on 2 functions for comparison
          also h(x) = sine + cosine
  • polar.gsp -- r()=asin(b -c)+d


Connect the Dots


Functions, Vocabulary     Quadratic Functions Exponent & Log Laws
Orientation, ... Higher Order Polynomials Trig Functions, "Before Unit Circle"
Calculator Resources Rationals Trig Functions, "Unit Circle & On"
Lines Log & Exponential Functions     Trig Cheat Sheet
[MC,i. Home] [Words] Classes spread sheet notes calc1

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3/2020, 9/2022, 10/2023, A. (A2) Azzolino
www.mathnstuff.com/math/precalc/pnotes5.htm