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
.
.