CK12 - Trigonometry

9. Answerswill vary. Examples:-240
   o
   , 480
   o


10. The frontwheelrotatesmore.It rotates100 revolutionsversus33.89revolutionsfor the backwheel,
    whichis a ~23800degreedifference.

Vocabulary

Acuteangle An acuteangleis an anglewith measurebetween0 and 90 degrees.

Anglesof rotationin standardpositionare co-terminalof they sharethe sameterminal

side.

Co-terminalangles

Minutes A minuteis 1/60 of a degree.

Obtuseangle An obtuseangleis an anglewith measurebetween90 and 180 degrees.

Protractor A protractoris a tool usedto measureangles.

A quadrantalangleis an anglein standardpositionwhoseterminalside lies on an

axis.

Quadrantalangle

Rightangle A right angleis an anglewith measureexactly90 degrees.

Seconds A secondis 1/60 of a minute,or 1/360of a degree.

An anglein standardpositionhas its initialside on the positivex-axis,its vertexat the

origin,and its terminalside anywherein the plane.A positiveanglemeansa counter-

Standardposition

clockwiserotation.A negativeanglemeansa clockwiserotation.

A straightangleis an anglewith measure180 degrees.A straightanglemakesa

straightline.

Straightangle

DefiningTrigonometricFunctions

Learningobjectives

A studentwill be able to:

• Find the valuesof the six trig functionsfor anglesin right triangles.


• Find the valuesof the six trig functionsfor anglesof rotation.


• Work with anglesin the unit circle.

Introduction

Considera situationin whichyou are buildinga rampso that peoplein wheelchairscan accessa building.

If the rampmusthavea heightof 8 feet, and the angleof the rampmustbe about 5
o
, how long mustthe
rampbe?

Solvingthis kind of problemrequirestrigonometry. Recallthat in the first lesson,you learnedthat the word
trigonometrycomes fromtwo wordsmeaning triangleandmeasure.In this lessonwe will definesix
trigonometricfunctions.For eachof thesefunctions,the elementsof the domainare angles.We will define
thesefunctionsin two ways:first, usingright triangles,and second,usinganglesof rotation.Oncewe have
definedthesefunctions,we will be able to solveproblemslike the one above.(We will, in fact, solvesuch