Chapter 1.6 Trigonometric Functions

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Chapter 1.6 Trigonometric Functions. The Unit Circle. Degree/Radian Conversion. To convert a degree measure to radians, multiply by π radians180° To convert a radian measure to degrees, multiply by 180°π radians. Examples. Examples 1) 120 ° 2) -45 ° 3) 5π6 4) -3π2. - PowerPoint PPT Presentation

Transcript of Chapter 1.6 Trigonometric Functions

Chapter 1.6 Trigonometric Functions

Chapter 1.6 Trigonometric FunctionsThe Unit Circle

Degree/Radian ConversionTo convert a degree measure to radians, multiply by radians180

To convert a radian measure to degrees, multiply by 180 radians

ExamplesExamples 1) 1202) -453) 564) -32

Radian MeasureThe RADIAN MEASURE of the angle ACB at the center of the unit circle equals the length of the arc that ACB cuts from the unit circle. Radius =1

Finding Arc LengthFind the length of an arc on a circle of radius 3 by a central angle of measure 2/3.S = r = 3(2/3) = 2An Angle In Standard Position

When an angle of measure is placed in standard position at the center of a circle of radius r, the six trigonometric functions of are defined as follows:

sin = y/rcsc = r/y

Cos = x/rsec = r/x

Tan = y/xcot = x/y(SOHCAHTOA)Sin opp/hypCos adj/hypTan opp/adjCsc hyp/oppSec hyp/adjCot adj/oppGraph of sin

Graph of cos

Graph of tan

PeriodicityPeriodic Function, Period: A function f(x) is periodic if there is a postive number p such that f(x + p) = f(x) for every value of x. The smallest such value of p is the period of f.Transformations of Trigonometric GraphsY = a f ( b ( x + c ) ) + dA = vertical stretch or shrink/reflection about x-axisB = horizontal stretch or shrink/ reflection about y-axisC = Horizontal shiftD = vertical shift

Finding Angles in degrees and RadiansFind the measure of cos-1 (-0.5) in degrees and radians.Put the calculator in degree mode and enter cos-1 (-0.5). You will get 120 degrees. Using the Inverse Trigonometric FunctionsSinx = 0.7Take the sin-1 of both sides.X = sin-1(0.7)X = 0.775HomeworkQuick Review pg 52 # 1-4Section 1.6 Exercises pg 52 #1-10