Sullivan Algebra and Trigonometry: Section 6.4 Trig Functions of General Angles

1
Sullivan Algebra and Trigonometry Section
6.4Trig Functions of General Angles

• Objectives of this Section
• Find the Exact Value of the Trigonometric
  Functions for General Angles
• Determine the Sign of the Trigonometric
  Functions of an Angle in a Given Quadrant
• Use Coterminal Angles to Find the Exact Value of
  a Trigonometric Function
• Find the Reference Angle of a General Angle
• Use the Theorem of Reference Angles

2
provided no denominator equals 0.
3
y
x
r
(a, b)
4
Find the exact value of each of the six
trigonometric functions of a positive angle
if (-2, 3) is a point on the terminal side.
y
(-2, 3)
x
5
(No Transcript)
6
y
x
P (1, 0)
P (a, b)
7
y
P (0,1)
x
8
(No Transcript)
9
y
a gt 0, b gt 0, r gt 0
a lt 0, b gt 0, r gt 0
x
r
(a, b)
a lt 0, b lt 0, r gt 0
a gt 0, b lt 0, r gt 0
10
y
x
11
Two angles in standard position are said to be
coterminal if they have the same terminal side.
y
x
12
Let denote a nonacute angle that lies in a
quadrant. The acute angle formed by the terminal
side of and either the positive x-axis or
the negative x-axis is called the reference angle
for
Reference Angle
13
Finding the reference angle
2. Determine the quadrant in which the terminal
side of the angle formed by the angle lies.
14
y
x
15
Reference Angles
16
Find the exact value of each of the following
trigonometric functions using reference angles
17
(No Transcript)