Trigonometric Functions with Quadrantal Angles
Do Now
The terminal side of angle
θ
in standard position passes through
the point (12, 16). Find the value of the six trigonometric
functions of angle
θ
.
Section 1.3
Trigonometric Functions
Objective:
SWBAT use trigonometric functions
with quadrantal angles.
Quadrantal Angles
Quadrantal Angle
: An angle whose terminal side
is on an axis.
Think about x or y equaling 0. What would happen to
the value of r in your trigonometric functions?
5.2-4
Example 1
F
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F
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C
T
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V
A
L
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Q
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A
D
R
A
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T
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G
L
E
S
The terminal side passes
through (0, 1). So
x
= 0,
y
= 1,
and
r
= 1.
Find the values of the six trigonometric functions for an
angle of 90
°.
Example 2
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x
=
–3
,
y
= 0, and
r
= 3.
Find the values of the six
trigonometric functions for an
angle
θ
in standard position with
terminal side through
(–3, 0).
Undefined Function Values
•
If the terminal side of a quadrantal angle lies
along the
y
-axis, then the tangent and secant
functions are undefined.
•
If the terminal side of a quadrantal angle lies
along the
x
-axis, then the cotangent and
cosecant functions are undefined.
Commonly Used Function Values
Commonly Used Function Values
u
n
d
e
f
i
n
e
d
1
u
n
d
e
f
i
n
e
d
0
1
0
0
csc
sec
cot
tan
cos
sin
Using a Calculator
•
A calculator in degree
mode returns the correct
values for sin 90
° and cos
90°.
•
The second screen shows
an ERROR message for tan
90° because 90° is not in
the domain of the tangent
function.
Caution
One of the most common errors involving
calculators in trigonometry occurs when
the calculator is set for radian measure,
rather than degree measure.
Homework:
Page 25 #’s 34-42 (evens)
Explore how to find the value of the six trigonometric functions for angles passing through specific points in standard position. Learn about quadrantal angles, their function values, and how calculators help in trigonometry. Avoid common errors related to calculator settings for degree or radian measures.
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Presentation Transcript
Do Now The terminal side of angle in standard position passes through the point (12, 16). Find the value of the six trigonometric functions of angle .
Section 1.3 Trigonometric Functions Objective: SWBAT use trigonometric functions with quadrantal angles.
Quadrantal Angles Quadrantal Angle: An angle whose terminal side is on an axis. Think about x or y equaling 0. What would happen to the value of r in your trigonometric functions?
FINDING FUNCTION VALUES OF QUADRANTAL ANGLES Example 1 Find the values of the six trigonometric functions for an angle of 90 . The terminal side passes through (0, 1). So x = 0, y = 1, and r = 1. undefined undefined 5.2-4
FINDING FUNCTION VALUES OF QUADRANTAL ANGLES Example 2 Find the values of the six trigonometric functions for an angle in standard position with terminal side through ( 3, 0). x = 3, y = 0, and r = 3. undefined undefined
Undefined Function Values If the terminal side of a quadrantal angle lies along the y-axis, then the tangent and secant functions are undefined. If the terminal side of a quadrantal angle lies along the x-axis, then the cotangent and cosecant functions are undefined.
Commonly Used Function Values sin cos tan cot sec csc 0 0 1 0 undefined 1 undefined 90 1 0 undefined 0 undefined 1 180 1 1 0 0 undefined undefined 270 1 1 0 undefined 0 undefined 360 0 1 0 undefined 1 undefined
Using a Calculator A calculator in degree mode returns the correct values for sin 90 and cos 90 . The second screen shows an ERROR message for tan 90 because 90 is not in the domain of the tangent function.
Caution One of the most common errors involving calculators in trigonometry occurs when the calculator is set for radian measure, rather than degree measure.
Homework: Page 25 # s 34-42 (evens)
