NAME INTRO TO TRIG UNIT 7 GRAPHING TRIG FUNCTIONS
NAMEINTRO TO TRIGUNIT 7GRAPHING TRIG /262/27PAGETOPIC2,3 The Sin graphThe Cos graph4,5 Investigation of Amplitudes6Investigation of Frequencies7Finding periods and sketchinggraphsxGraphing Sin and CosQUIZWINER BREAK8xGraphing TanMore Tan and Review of all trigfunctionsREVIEWTEST1HOMEWORKNo HomeworkAMPLITUDE Homework WorksheetFREQUENCY Homework WorksheetPERIOD Homework WorksheetNo HomeworkRelax and enjoy your breakNo HomeworkFINISH REVIEW!STUDYNO HOMEWORK!
Graphing Sin xIn order to graph y sin x, we will use the x-axis as a number line in terms of pi.We will start by filling in the chart below:X(radians)0/6/3/22 /35 /67 /64 /3X(degrees)Sin xNow we will take the values that we just found and sketch a graph.**This curve represents the basic sinecurve.Fill in the questions below using Increases or DecreasesFrom 0 to pi/2 (quadrant I), sin x from 0 to 1.From pi/2 to pi (quadrant II), sin x from 1 to 0.From pi to 3pi/2 (quadrant III), sin x from 0 to –1.From 3pi/2 to 2pi (quadrant IV), sin x from –1 to 0.23 /25 /311 /62
Graphing Cos xNow we will do the same thing for the graph of Cos xX(radians)0/6/3/22 /35 /67 /64 /3X(degrees)COS xFill in the questions below using Increases or DecreasesFrom 0 to pi/2 (quadrant I), cos x from 0 to 1.From pi/2 to pi (quadrant II), cos x from 1 to 0.From pi to 3pi/2 (quadrant III), cos x from 0 to –1.From 3pi/2 to 2pi (quadrant IV), cos x from –1 to 0.33 /25 /311 /62
Investigation of AmplitudeThe basic Sine and Cosine graphs can be manipulated by changing a and b in the equationsbelow:Y a Sin bx andy a Cos bxUse your Graphing Calculator to find out what the “a” does to the graph:STEP 1: Graph y sinx (in this case a 1)Change your window. Your x-min should be 0, x-max should be 2π, y-min shouldbe -5, y-max should be 5.Go to y and input SinxHit GRAPHSTEP 2: Investigate the graph of y sinxWhat is the maximum value of the graph?What is the minimum value of the graph?When does the graph hit the x-axis (in terms of π)?STEP 3: Graph y 2sinx (a 2)What is the maximum value of the graph?What is the minimum value of the graph?When does the graph hit the x-axis (in terms of π)?STEP 4: Graph y 3sinx (a 3)What is the maximum value of the graph?What is the minimum value of the graph?When does the graph hit the x-axis (in terms of π)?STEP 5: Make a conjecture (best guess) about the effect of “a” on the graph of theequation y asinx4
STEP 6: Test your guess by predicting the maximum and minimum values for the graphsbelow:Y 1/2 sinxy 4sinxMax:Max:Min:Min:STEP 7: Think about what would happen if “a” was negative.Graph y -sinxGraph y -2sinxWhat happens?STEP 8: Make a sketch.Sketch all of the graphs above and label them.What Equations are “missing” if you wanted to “complete” the picture?1.2.3.5
INVESTIGATION OF FREQUENCYThe basic Sine and Cosine graphs can be manipulated by changing a and b in the equationsbelow:Y a Sin bx andy a Cos bxUse your Graphing Calculator to find out what the “b” does to the graph:STEP 1: Graph y sinx (in this case b 1)Your x-min should be 0, x-max should be 2π, y-min should be -5, y-max should be5.Go to y and input SinxHit GRAPHSketch the basic sin curve from 0-2π:STEP 2: Graph y sin2xHow many sin curves do you see?STEP 3: Graph y sin3xHow many sin curves do you see?STEP 4: Make a Conjecture (best guess) as to what effect “b” has on the graph:STEP 5: Testing your conjectureSketch what you think y sin(1/2)x will look like:Now graph y sin(1/2)x in your graphing calculator. Were you right?STEP 6: Sketching more graphsSketch y sin4x:6
THE PERIOD OF A GRAPHBased on what we’ve learned we know that“a” is for and determines the ofthe graph.“b” is for and determines the number of curvesbetween andThe Period of a graph is .To find the period of a graph use:To determine what interval to use on the x-axis:1.) y 3cos1/2xAmplitude:2.) y d:x-interval:x-interval:3.) Sketch the graph of the curve y 2cos2x:4.) Sketch the graph of the curve y -sin1/2x:7
GRAPHING TAN FUNCTIONStart out by making sure that your mode is set to degrees.Now set up your window as follows:Xmin: -2πXmax: 2πYmin: -3Ymax: 31.) In the "Y " menu, type "Tan(x)To see the graph use the "graph" key.2.) There will be several vertical lines on the graph. These lines are called3.) At the asymptotes for the function y tan(x) is4.) What are the x values for these asymptotes?5.) What are the values for when y 0?6.) What are the Max and min of the graph?7.) Sketch the graph below:8
The basic Sine and Cosine graphs can be manipulated by changing a and b in the equations below: Y a Sin bx and y a Cos bx Use your Graphing Calculator to find out what the “a” does to the graph: STEP 1: Graph y sinx (in this case a 1) Change your window. Your x-min should be 0, x
CONCEPT IN SOLVING TRIG EQUATIONS. To solve a trig equation, transform it into one or many basic trig equations. Solving trig equations finally results in solving 4 types of basic trig equations, or similar. SOLVING BASIC TRIG EQUATIONS. There are 4 types of common basic trig equations: sin x a cos x a (a is a given number) tan x a cot x a
Solving trig inequalities finally results in solving basic trig inequalities. To transform a trig inequality into basic ones, students can use common algebraic transformations (common factor, polynomial identities ), definitions and properties of trig functions, and trig identities, the most needed. There are about 31 trig identities, among them
Unit 4 – Trig Functions Unit 5 – Trig Identities Spring Semester Unit 6 – Polar Unit 7 – Complex Numbers Unit 8 – Vectors Unit 9 – Conics Unit 10 – Partials and Matrices Unit 11 – Sequence and Series Unit 12 – Intro to Calculus Online Learning and Microsoft Teams: This class will be taught in a “Flipped Classroom” format.
Trigonometry (on a very basic level) trigonometric relations in right angles, values and properties of trig functions, graphing trig functions, using trig identities, solving trig equations What Not to Study Trigonometry beyond the very basics. However, you should know: SOH-CAH-TOA how to solve right triangles the unit circle
1 Algebra2/Trig Chapter 13 Packet In this unit, students will be able to: Use the reciprocal trig identities to express any trig function in terms of sine, cosine, or both. Prove trigonometric identities algebraically using a variety of techniques Learn and apply the cofunction property Solve a linear trigonometric function using arcfunctions
Derivatives of Trig Functions – We’ll give the derivatives of the trig functions in this section. Derivatives of Exponential and Logarithm Functions – In this section we will get the derivatives of the exponential and logarithm functions. Derivatives of Inverse Trig Functions – Here we will look at the derivatives of inverse trig functions.
Alg/Trig is not taken in 11th grade, a math based class in 12th grade is required 3.0 or 4.0* and Advanced Alg/Trig. and above. Algebra/Trig is the MINIMUM! If math beyond Alg/Trig is not taken in 11th grade, a math based class in 12th grade is required Health & Physical Education 1 Healt
Part 3: Determine the Value of Trig Ratios for a Double Angle If you know one of the primary trig ratios for any angle, then you can determine the other two. You can then determine the primary trig ratios for this angle doubled. Example 2: If cosH ) I and 0 H 28, determine the value of cos(2H) and sin(2H)
