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## 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

## 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
 Digital Manipulatives -- Dynamic Tokens sinelaw.xls DIGITAL MANIPULATIVE jig1.xls -- UNIT CIRCLE PUZZLE

 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

 Sketch Pads -- Dynamic Analytic Geometry Angles NewCentral   -- One or 2 angles in standard position. radianSector   -- arc length, sector area, radians 30° 45° 60° 90° pdf questions,   30° 45° 60° 90° pdf answers 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
 © 3/2020, 9/2022, 10/2023, A. (A2) Azzolino www.mathnstuff.com/math/precalc/pnotes5.htm