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Chapter 2 Section 2
 Radius = 1
 Center at Origin (0,0)
 Circumference = 2𝜋𝑟
If x = 0, then tangent and
secant are undefined
If y = 0, then cotangent and
cosecant are undefined
 Find the values of the six trigonometric functions using a point on the unit circle
𝟏
𝟐
 Let 𝑡 be a real number and let 𝑷 = − ,
𝟑
𝟐
be the point on the unit circle that corresponds to 𝑡.
 Find the values of
sin 𝑡 =
csc(𝑡) =
cos 𝑡 =
sec(𝑡) =
tan(𝑡) =
cot(𝑡) =
 Let 𝑃 = (𝑥, 𝑦) be a point on the unit circle that corresponds to the real number 𝑡
 Let 𝜃 (in radians) be the angle in standard position and subtends the arc of length 𝑠
 Since the unit circle has radius 1, then 𝑠 = |𝑡| and arc length 𝑠 = 𝑟|𝜃|, then 𝜃 = 𝑡
 Let 𝑃 = (𝑥, 𝑦) be a point on the unit circle that corresponds to the real number 𝑡
 Let 𝜃 (in radians) be the angle in standard position and subtends the arc of length 𝑠
 Since the unit circle has radius 1, then 𝑠 = |𝑡| and arc length 𝑠 = 𝑟|𝜃|, then 𝜃 = 𝑡
 Let 𝑃 = (𝑥, 𝑦) be a point on the unit circle that corresponds to the real number 𝑡
 Let 𝜃 (in radians) be the angle in standard position and subtends the arc of length 𝑠
 Since the unit circle has radius 1, then 𝑠 = |𝑡| and arc length 𝑠 = 𝑟|𝜃|, then 𝜃 = 𝑡
This allows us to define sin 𝑡 = sin(𝜃)
 Multiples of Quadrantal Angles
 Find the exact values of the trigonometric functions of
𝜋
4
= 45°
 Find the exact values of the trigonometric functions of
𝜋
4
= 45°
 Be sure you know how to change your calculator to Radians or Degrees
(a) cos 48° = 0.67
(b) csc 21° =
(a) tan
𝜋
12
1
sin(21°)
= 0.27
= 2.79
Can use any
circle whose
center is at
the origin
This works by way of similar triangles
OA*P* and OAP
Ratios of corresponding sides are equal
Can use any
circle whose
center is at
the origin
 Find the exact values of each of the six trigonometric functions of an angle 𝜃 if
(4, −3) is a point on its terminal side in standard position
Calculate the time T for 𝜃 = 30°.
How long is Sally on the paved road?