    ### TAN GENTS    AND OTHER THINGS OF INTEREST

 Contents of This Page Interactive Trig Sketch Pad Material - Right Triangle Trig - Radians - Unit Circle & Pythagoresn Identities - Polar Graphing Spread Sheets -- Dynamic Computation - Right Triangle Trig - Graphs of Trig Functions - Solve triangles - Use Sine Law & Cosine Law - Graphs y=Asin(Bx-C) +D - Graph & Compair Two Trig Functions - Sine Law Digital Manipulative Triangle Vocabulary- includes Greek letter notation Right Triangle Sides & Angles- 7th - 10th-grade work sets stage for Trig 30°-45°-60°-90° Angles- from the equalateral triangle and quadraleteral Unit Circle - a circle with a radius of 1 for easy computation - trig definitions Pythagorean Trig Identities - through a unit circle Vocabulary - trig functions Special Angles - in all quadrants Fractions then Radian Measure - Name improper fractions from 0 through 2 - Use these fraction to name radian angle measures Sine Law - ambiguous case Trig Fx Translations, Etc. Solve Triangles Vector Addition - w/paper, w/spreadsheet, w/html Trig Cheat Sheets special angles, etc. identities Proof of the Sine of the Sum and the Cosine of the Sum Trig Tables Short Tables for Graphing of Sine, Cosine, Tangent, Etc. sine & cosine tangent & cotangent Arc Functions - inverse trig functions Connect-the-Dots Puzzles

 Stuff on Other Pages  Visit the Interactive Sketch Pad Material On This Topic 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 Radians radianSector   -- arc length, sector area, radians 30° 45° 60° 90° pdf questions, 30° 45° 60° 90° pdf answers Unit Circle and Identities 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 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 SinTraceDerSum -- Sine from many views, right triangle, ABCD, derivative, antiderivative polar.gsp -- r( )=asin(b -c)+d  Spread Sheets -- Dynamic Computation sine.xls Graphs y=Asin(Bx-C) +D, where A, B, C, D are input values. Scatter-Plots y=Atan(Bx-C)+D, where A, B, C, D are input values. Graphs two sine functions where A, B, C, D are input values. Graphs one sine function and one cosine function where where A, B, C, D are input values. solvtrg.xls Solve a right triangle. Solve a 45-45-90 triangle. Input leg a. Seek a leg and hypotenuse. Input side c. Seek two legs. Solve a 30-60-90 triangle. Input leg a. Seek a leg and hypotenuse. Input leg b. Seek a leg and hypotenuse. Input side c. Seek the hypotenuse. Use Pythagorean Theorem and arithmetic and basic trig. Input leg a and leg b. Seek the hypotenuse and the angles. Input hypotenuse c and leg a. Seek a leg and the angles. Input angle A and side a. Seek a leg, side, and hypotenuse. Solve any triangle. Use the Sine Law, if a side and the opposite angle are given. Input angles A , B, side a. Seek two sides and an angle. Input angle A , side a, side b. Seek two angles and a side. Use the Law of Cosines. Input sides a, b, c. Seek each angle. Input angle A , sides b,c. Seek no solution, 1 solution, or 2 solutions. sinelaw.xls -- sine law digital manipulative

 Triangle Sides & Angles Vocabulary opposite adjacent hypotenuse , alpha, the Greek letter , theta, the Greek letter , gamma, the Greek letter  Right Triangle Sides & Angles Equilateral Triangle 60-60-60 triangle, 30-60-90 triangle Equilateral Quadrilateral the square, 45-45-90 triangle

 Fractions, Radians, Angles

 Trig Functions of Reference  &   Special Angles trig30s trig45s trig60s trig90s Veronica's Bow Tie and All Students Take Calculus Worksheet - Trig Functions Signs in All Quadrants Quadrantals Worksheet

 Six Trig Functions and the Unit Circle The Animated Unit Circle. - Words w/text. - Function Library sine.xls -- sine, cosine, tangent, or sine & cosine Each function is the length of a leg or hypotenuse of a right triangle. Unit Circle w/6 Trig Functions Unit Circle & Angle Unit Circle & Sine & Cosine Unit Circle & Tangent & Secant Unit Circle & Cotangent & Cosecant central angle animation only sine & cosine animation only tangent and secant animation only cotangent and cosecant animation only all 6 functions animation only all 6 functions with segments labeled animation only

 Inverse Trig Functions

 Pythagorean Trig Identities Pythagorean Identitiessine-cosine, sin2(A) + cos2(A) = 1 tangent-secant, tan2(A) + 1 = sec2(A) cotangent-cosecant, cot2(A) + 1 = csc2(A)

 Cheat Sheets of Trig Identities Proof of the Sine of the Sum and the Cosine of the Sum trig identities sheet 1- Pythagorean Identities, Cofunctions, Odd/Even Functions trig identities sheet 2- Sine, Cosine, & Tangent of the Sums & Differences trig identities sheet 3- Double & Half Angle Formulas trigstud (Signs of the Trig Functions)- All Students Take Calculus

 Sine Law Sine Law, Ambiguous Case, Pictorial & Concrete Representation - just the pictorial graphic - just the master sinelaw.xls -- sine law digital manipulative

 Connect the Dots

 Vector Addition, use components to compute the resultant vector.xls -- completes scalar addition, multiplication, and vector addition. polrect.xls -- A DIGITAL MANIPULATIVE for drawing and addition of vectors.

 Vocabulary central angle chord cos cosecant cosine cot, cotangent csc period Pythagorean Theorem radian reference angle revolution sec, secant sin, sine special angle tan, tangent trigonometric trigonometry       © 2015, 2017, 2019 Agnes Azzolino www.mathnstuff.com/math/spoken/here/2class/330/c33pg00.htm