Download Section 5.3 Trigonometric Functions of Any Angle

Section 5.3 Trigonometric
Functions of Any Angle
Objective: In this lesson you learned
how to evaluate trigonometric
functions of any angle.
Important Vocabulary Define each
term or concept.
• Reference angles
• Period
I. Introduction
• Let θ be an angle in standard position with (x, y)
a point on the terminal side of θ and
r x y 0
2
2
Complete the following
definitions of the
trigonometric functions
of any angle:
opp
sin  
hyp
y
r
y
x
r
x
y
r
x
x
r
x
y
r
y
• Name the quadrants in which
the sine function is positive.
• Name the quadrants in which
the sine function is negative.
• Name the quadrants in which
the cosine function is
positive.
• Name the quadrants in which
the cosine function is
negative.
• Name the quadrants in which
the tangent function is
positive.
• Name the quadrants in which
the tangent function is
negative.
What's your
sign?
Example 1
1
sin  
2
Θ lies in either
I or IV
Important Vocabulary Define each
term or concept.
• Reference angles
Let θ be an angle in standard position. Its reference
angle is the acute angle θ’ formed by the terminal
side and the horizontal axis (page 390)
• Period
II. Reference Angles
Example 2
To find the value of a trigonometric
function of any angle θ, . . .
Example 3
III. Trigonometric Functions of
Real Numbers
• The sine function’s domain is
______________ and its range is
___________.
• The cosine function’s domain is
____________ , and its range is
_________ .
• The period of the sine function is _______.
The period of the cosine function is
___________ .
Even and Odd
• Which trigonometric functions are even
functions?
cos(t )  cos t
sec(t )  sec t
• Which trigonometric functions are odd
functions?
sin(t )   sin t
csc(t )  csc t
tan(t )   tan t
cot(t )  cot t
Homework
• Pg 397: #1, 3, 7, 13-19 all, 21, 23, 24,
25, 27, 29, 33, 39-53 odd
• Pg 398: #57, 59, 61, 65, 67, 69, 71, 75
77, 79, 81, 83, 85, 87, 91, 97, 99, 101, 103