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Trigonometry

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Sine= opposite / hypotenuse. Cosine= adjacent / hypotenuse. Tangent= opposite / adjacent ... The terminal side of the angle, ?, intersects the unit circle at a ... – PowerPoint PPT presentation

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Title: Trigonometry

1
Trigonometry
• Circular Functions
• By Miller Wright

2
Objective
• Further generalize the trigonometric functions by
defining them in terms of the unit circle.

3
Recollection
• From Lesson 13-3
• cos ? y/r and sin ? x/r.
• If we are only working with the unit circle then
r always equals 1. Therefore, cos ? y and sin ?
x.

4
Definitions and Formulas
• Sine opposite / hypotenuse
• Sine? Y
• Cosine? X

5
Solving For A Point, P
• The terminal side of the angle, ?, intersects the
unit circle at a unique point, P(x,y). Recall
P(x,y) is on a unit circle where r 1, sin ?y
and cos ?x.
• If the terminal side of an angle ? in standard
position intersects the unit circle at P(x,y),
then cos ? x and sin ? y. Therefore, the
coordinates of P can be written as P(cos ?, sin
?).

(0,1)

P(co?,sn ?)
?
(1,0)
(-1,0)
(0,-1)
6
Circular Functions
• Since there is one point P for any angle, the
relations cos ?x and sin ?y are functions of ?.
Because they are both based on a unit circle they
are called circular functions.

?
Theta
7
Periodic Functions
Cosine Curve
Sine Curve
8
Periodic Functions
• A function is called periodic if there is a
number a such that f(x)f(xa) for all x in the
domain of the function. The least positive value
of a for which f(x)f(xa) is called the period
of the function.