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CHAPTER

TRIGONOMETRIC FUNCTIONS:

5

UNIT CIRCLE APPROACH

LEARNING OUTCOMES By the end of this chapter, you should be able to

 Use reference number to find terminal point on the unit circle.  Determine trigonometric function using properties of unit circle.  Evaluate trigonometric function using definition of trigonometric functions.  Sketch and transform graphs of sine, cosine, tangent, secant and cosecant. 5.1

UNIT CIRCLE This section is about properties of circle radius 1 unit and centred at the origin. The definition of unit circle is, Definition: Unit Circle The unit circle is the circle in

xy 

plane centred at origin and has one unit

radius. The equation for unit circle is x2  y2  1

Example 1: Verify that the point

 2 6 5 P  ,  7 7 

is on the unit circle.

Solution We must verify that P satisfies equation of unit circle,

Since

and 2 6 x 7

5 y 7

, substitute into

x2  y2  1

x2  y2  1

Hence, 2

 2 6   5  2 24 25       1    7 7 49 49  

1

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