Download CLASS 1 CHARACTERISTICS of FUNCTIONS, ALGEBRAICALLY

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

page
1
page
2
page
3
page
4
page
5
page
6
page
7
page
8
page
9
page
10
page
11
page
12
page
13
page
14
Document related concepts
no text concepts found
Transcript 
Chapter 5 – Trigonometric Functions:
Unit Circle Approach
5.2 - Trigonometric Function of Real Numbers
Definition of the Trig Functions
5.2 - Trigonometric Function of Real Numbers
Example – pg. 384

Find sin t and cos t for the values of t whose terminal
points are shown on the unit circle in the figure. t
increases in increments of /4.
5.2 - Trigonometric Function of Real Numbers
Special Values
5.2 - Trigonometric Function of Real Numbers
Domains of the Trig Functions
Function
sin, cos
Domain
All real numbers

tan, sec
All real numbers other than  n
2
for any integer n
cot, csc
All real numbers other than n for
any integer n
5.2 - Trigonometric Function of Real Numbers
Signs of the Trig Functions
Quad
I
II
III
IV
Positive Functions
All
sin, csc
tan, cot
cos, sec
5.2 - Trigonometric Function of Real Numbers
Negative Functions
None
cos, sec, tan, cot
sin, csc, cos, sec
sin, csc, tan, cot
Example – pg. 384

Find the exact value of the trigonometric functions at
the given real number.
5.2 - Trigonometric Function of Real Numbers
Examples – pg. 385

Find the sign of the expression if the terminal point
determined by t is in the given quadrant.
tan t sin t
49.
, Quadrant III
cot t
50. cos t sec t , any quadrant
5.2 - Trigonometric Function of Real Numbers
Even-Odd Properties
Sine, cosecant, tangent, and cotangent are odd
functions.
 Cosine and secant are even functions.

sin  t    sin t
cos  t   cos t
tan  t    tan t
csc  t    csc t
sec  t   sec t
cot  t    cot t
5.2 - Trigonometric Function of Real Numbers
Example – pg. 384

Find the exact value of the trigonometric functions at
the given real number.
5.2 - Trigonometric Function of Real Numbers
Fundamental Identities

Reciprocal Identities
1
1
csc t 
sec t 
sin t
cos t
sin t
tan t 
cos t

1
cos t
cot t 
=
tan t sin t
Pythagorean Identities
sin 2 t  cos 2 t  1
tan 2 t  1  sec2 t
5.2 - Trigonometric Function of Real Numbers
1+ cot 2 t  csc2 t
Examples – pg. 385

Write the first expression in terms of the second if the
terminal point determined by t is in the given
quadrant.
5.2 - Trigonometric Function of Real Numbers
Examples – pg. 385

Find the values of the trigonometric functions of t
from the given information.
5.2 - Trigonometric Function of Real Numbers
Examples – pg. 384

Find the exact value of the trigonometric functions at
the given real number.
5.2 - Trigonometric Function of Real Numbers
Related documents