Previous: Trigonometric functions of an angle

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MTH 110 Elementary Functions Trigonometric
Functions of Real Numbers

• Previous Trigonometric functions of an angle
• Reformulate definitions Trigonometric functions
  of real numbers
• Method - unit circle

y
P(t) (x,y)
(1,0)
x
2
Trigonometric Functions of Real Numbers

• If t gt 0, P(t) is at a distance of t units from
  (1,0) along an arc of the circle in a
  counterclockwise direction.
• If t lt 0, P(t) is at a distance of t units
  from (1,0) along an arc of the circle in a
  clockwise direction.

y
y
P(t) (x,y)
(1,0)
(1,0)
x
x
P(t) (x,y)
3
Example 1

• Find the rectangular coordinates of each of the
  following points in the unit circle
• a. P(0) b. P(?/2) c. P(- ?/2)

y
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Example 1

• Find the rectangular coordinates of each of the
  following points in the unit circle
• a. P(0) b. P(?/2) c. P(- ?/2)

y
P(?/2) (0,1)
P(0) (1,0)
P(-?/2) ?
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Trigonometric Functions of Real Numbers

• The number t 2? corresponds to the same point
• on the unit circle as t

y
P(t) (x,y) P(t 2?)
(1,0)
x
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Trigonometric Functions of Real Numbers

• Definition For any real number t, let P(t)
  (x, y)
• be a point on the unit circle that corresponds to
  t according
• to the wrapping function. The six trigonometric
  functions
• of t are as follows
• sin t y
• cos t x
• tan t y/x
• cot t x/y
• sec t 1/x
• csc t 1/y

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Homework
P. 438, 3, 5, 7, 9, 11, 17, 21, 22, 24, 30, 32