1. Home
  2. Precalculus
  3. Precalculus
  4. Basic functions and identities

0.1 Basic functions and identities

<< Chapter < Page
  Precalculus   Page 1 / 1
Chapter >> Page >

Graphs of the parent functions

Three graphs side-by-side. From left to right, graph of the identify function, square function, and square root function. All three graphs extend from -4 to 4 on each axis.
Three graphs side-by-side. From left to right, graph of the cubic function, cube root function, and reciprocal function. All three graphs extend from -4 to 4 on each axis.
Three graphs side-by-side. From left to right, graph of the absolute value function, exponential function, and natural logarithm function. All three graphs extend from -4 to 4 on each axis.

Graphs of the trigonometric functions

Three graphs of trigonometric functions side-by-side. From left to right, graph of the sine function, cosine function, and tangent function. Graphs of the sine and cosine functions extend from negative two pi to two pi on the x-axis and two to negative two on the y-axis. Graph of tangent extends from negative pi to pi on the x-axis and four to negative 4 on the y-axis.
Three graphs of trigonometric functions side-by-side. From left to right, graph of the cosecant function, secant function, and cotangent function. Graphs of the cosecant function and secant function extend from negative two pi to two pi on the x-axis and ten to negative ten on the y-axis. Graph of cotangent extends from negative two pi to two pi on the x-axis and twenty-five to negative twenty-five on the y-axis.
Three graphs of trigonometric functions side-by-side. From left to right, graph of the inverse sine function, inverse cosine function, and inverse tangent function. Graphs of the inverse sine and inverse tangent extend from negative pi over two to pi over two on the x-axis and pi over two to negative pi over two on the y-axis. Graph of inverse cosine extends from negative pi over two to pi on the x-axis and pi to negative pi over two on the y-axis.
Three graphs of trigonometric functions side-by-side. From left to right, graph of the inverse cosecant function, inverse secant function, and inverse cotangent function.

Trigonometric identities

Pythagorean Identities cos 2 t + sin 2 t = 1 1 + tan 2 t = sec 2 t 1 + cot 2 t = csc 2 t
Even-Odd Identities cos (− t ) = cos   t sec (− t ) = sec   t sin (− t ) = − sin   t tan (− t ) = − tan   t csc (− t ) = − csc   t cot (− t ) = − cot   t
Cofunction Identities cos   t = sin ( π 2 − t ) sin   t = cos ( π 2 − t ) tan   t = cot ( π 2 − t ) cot   t = tan ( π 2 − t ) sec   t = csc ( π 2 − t ) csc   t = sec ( π 2 − t )
Fundamental Identities tan   t = sin   t cos   t sec   t = 1 cos   t csc   t = 1 sin   t cot   t = 1 tan   t = cos   t sin   t
Sum and Difference Identities cos ( α + β ) = cos   α   cos   β − sin   α   sin   β cos ( α − β ) = cos   α   cos   β + sin   α   sin   β sin ( α + β ) = sin   α   cos   β + cos   α   sin   β sin ( α − β ) = sin   α   cos   β − cos   α   sin   β tan ( α + β ) = tan   α + tan   β 1 − tan   α   tan   β tan ( α − β ) = tan   α − tan   β 1 + tan   α   tan   β
Double-Angle Formulas sin ( 2 θ ) = 2   sin   θ   cos   θ cos ( 2 θ ) = cos 2 θ − sin 2 θ cos ( 2 θ ) = 1 − 2   sin 2 θ cos ( 2 θ ) = 2   cos 2 θ − 1 tan ( 2 θ ) = 2   tan   θ 1 − tan 2 θ
Half-Angle Formulas sin   α 2 = ± 1 − cos   α 2 cos   α 2 = ± 1 + cos   α 2 tan   α 2 = ± 1 − cos   α 1 + cos   α tan   α 2 = sin   α 1 + cos   α tan   α 2 = 1 − cos   α sin   α
Reduction Formulas sin 2 θ = 1 − cos ( 2 θ ) 2 cos 2 θ = 1 + cos ( 2 θ ) 2 tan 2 θ = 1 − cos ( 2 θ ) 1 + cos ( 2 θ )
Product-to-Sum Formulas cos   α   cos   β = 1 2 [ cos ( α − β ) + cos ( α + β ) ] sin   α   cos   β = 1 2 [ sin ( α + β ) + sin ( α − β ) ] sin   α   sin   β = 1 2 [ cos ( α − β ) − cos ( α + β ) ] cos   α   sin   β = 1 2 [ sin ( α + β ) − sin ( α − β ) ]
Sum-to-Product Formulas sin   α + sin   β = 2   sin ( α + β 2 )   cos ( α − β 2 ) sin   α − sin   β = 2   sin ( α − β 2 )   cos ( α + β 2 ) cos   α − cos   β = − 2   sin ( α + β 2 )   sin ( α − β 2 ) cos   α + cos   β = 2   cos ( α + β 2 )   cos ( α − β 2 )
Law of Sines sin   α a = sin   β b = sin   γ c a sin   α = b sin   β = c sin   γ
Law of Cosines a 2 = b 2 + c 2 − 2 b c   cos   α b 2 = a 2 + c 2 − 2 a c   cos   β c 2 = a 2 + b 2 − 2 a b   cos   γ

Questions & Answers

summarize halerambos & holbon
David Reply
the Three stages of Auguste Comte
Clementina Reply
what are agents of socialization
Antonio Reply
sociology of education
Nuhu Reply
definition of sociology of education
Nuhu
what is culture
Abdulrahim Reply
shared beliefs, values, and practices
AI-Robot
What are the two type of scientific method
ogunniran Reply
I'm willing to join you
Aceng Reply
what are the scientific method of sociology
Man
what is socialization
ogunniran Reply
the process wherein people come to understand societal norms and expectations, to accept society's beliefs, and to be aware of societal values
AI-Robot
scientific method in doing research
ogunniran
defimition of sickness in afica
Anita
Cosmology
ogunniran
Hmmm
ogunniran
list and explain the terms that found in society
REMMY Reply
list and explain the terms that found in society
Mukhtar
what are the agents of socialization
Antonio
Family Peer group Institution
Abdulwajud
I mean the definition
Antonio
ways of perceived deviance indifferent society
Naomi Reply
reasons of joining groups
SAM
to bring development to the nation at large
Hyellafiya
entails of consultative and consensus building from others
Gadama
World first Sociologist?
Abu
What is evolutionary model
Muhammad Reply
Evolution models refer to mathematical and computational representations of the processes involved in biological evolution. These models aim to simulate and understand how species change over time through mechanisms such as natural selection, genetic drift, and mutation. Evolutionary models can be u
faruk
what are the modern trends in religious behaviours
Selekeye Reply
what are social norms
Daniel Reply
shared standards of acceptable behavior by the group or appropriate behavior in a particular institution or those behaviors that are acceptable in a society
Lucius
that is how i understood it
Lucius
examples of societal norms
Diamond
Discuss the characteristics of the research located within positivist and the interpretivist paradigm
Tariro Reply
what is Industrialisation
Selekeye Reply
industrialization
Angelo
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Precalculus' conversation and receive update notifications?

Ask