Trigonometric Functions: The Unit Circle

1
Trigonometric Functions The Unit Circle

• Section 4.2

2
Objectives

• Find a point on the unit circle given one
  coordinate and the quadrant in which the point
  lies.
• Determine the coordinates of a point on the unit
  circle given a point on the unit circle.
• State the sign of the sine or cosine value of an
  angle based on the quadrant in which the terminal
  side of an angle occurs.
• State the sine and cosine values of an angle
  (measured in radians) where the angles have a
• measure of

3
Objectives

• Determine the tangent, cotangent, secant, and
  cosecant values of an angle given a point on the
  unit circle.
• State the sign of the tangent, cotangent, secant,
  and cosecant value of an angle based on the
  quadrant in which the terminal side of an angle
  occurs.
• Determine the tangent, cotangent, secant, and
  cosecant values of an angle (measured in radians)
  where the angles have a measure of

4
Vocabulary

• quadrant
• sine of an angle
• cosine of an angle
• terminal side of an angle
• initial side of an angle
• tangent of an angle
• cotangent of an angle
• secant of an angle
• cosecant of an angle

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Unit Circle
6
If the point is on the unit circle in
quadrant IV, then find y.
7
If P(t) has coordinates (0.141, 0.99), find the
coordinates of each point indicated below.
8
Find the terminal point P(x, y) on the unit
circle determined by the value of
9
If , find the sin(t) and cos(t).
10
If , find the sin(t) and cos(t).
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If , find the sin(t) and cos(t).
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Quotient Identities
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Reciprocal Identites
14
Pythagorean Identity