TrigFunctionsofSpecialAngles

# TrigFunctionsofSpecialAngles - Special Angles and their...

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Special Angles and their Trig Functions By Jeannie Taylor Through Funding Provided by a VCCS LearningWare Grant

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We will first look at the special angles called the quadrantal angles. 90 180 270 0 The quadrantal angles are those angles that lie on the axis of the Cartesian coordinate system: , , , and . 0 90 180 270
We also need to be able to recognize these angles when they are given to us in radian measure. Look at the smallest possible positive angle in standard position, other than 0 , yet having the same terminal side as 0 . This is a 360 angle which is equivalent to . radians 2 π radians 2 360 = 90 180 270 0 2 = radians If we look at half of that angle, we have radians or 180 . radians = Looking at the angle half-way between 180 and 360 , we have 270 or radians which is of the total (360 or ). 2 3 4 3 2 radians Moving all the way around from 0 to 360 completes the circle and and gives the 360 angle which is equal to radians. 2 radians 2 3 = Looking at the angle half-way between 0 and 180 or , we have 90 or . 2

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We can find the trigonometric functions of the quadrantal angles using this definition. We will begin with the point (1, 0) on the x axis. (1, 0) radians 2 π 0 radians radians 2 3 = radians radians 2 = 0 90 180 270 360 or As this line falls on top of the x axis, we can see that the length of r is 1. y x x y x r r x y r r y = = = = = = β cot tan sec cos csc sin For the angle 0 , we can see that x = 1 and y = 0. To visualize the length of r, think about the line of a 1 angle getting closer and closer to 0 at the point (1, 0). Remember the six trigonometric functions defined using a point ( x , y ) on the terminal side of an angle, .

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radians 2 π 0 radians radians 2 3 = radians radians 2 = 0 90 180 270 360 (1, 0) or undefined is 0 cot 0 1 0 0 tan 1 0 sec 1 0 cos undefined is 0 csc 0 0 sin = = = = = Using the values, x = 1, y = 0, and r = 1, we list the six trig functions of 0.
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## This note was uploaded on 01/12/2011 for the course MAT117 MAT 117 taught by Professor Ranjitrebello during the Spring '09 term at University of Phoenix.

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TrigFunctionsofSpecialAngles - Special Angles and their...

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