-
Home
- Algebra and trigonometry
- Periodic functions
- Inverse trigonometric functions
Visit
this website for additional practice questions from Learningpod.
Key concepts
- An inverse function is one that “undoes” another function. The domain of an inverse function is the range of the original function and the range of an inverse function is the domain of the original function.
- Because the trigonometric functions are not one-to-one on their natural domains, inverse trigonometric functions are defined for restricted domains.
- For any trigonometric function
if
then
However,
only implies
if
is in the restricted domain of
See
[link] .
- Special angles are the outputs of inverse trigonometric functions for special input values; for example,
See
[link] .
- A calculator will return an angle within the restricted domain of the original trigonometric function. See
[link] .
- Inverse functions allow us to find an angle when given two sides of a right triangle. See
[link] .
- In function composition, if the inside function is an inverse trigonometric function, then there are exact expressions; for example,
See
[link] .
- If the inside function is a trigonometric function, then the only possible combinations are
if
and
if
See
[link] and
[link] .
- When evaluating the composition of a trigonometric function with an inverse trigonometric function, draw a reference triangle to assist in determining the ratio of sides that represents the output of the trigonometric function. See
[link] .
- When evaluating the composition of a trigonometric function with an inverse trigonometric function, you may use trig identities to assist in determining the ratio of sides. See
[link] .
Section exercises
Verbal
Why do the functions
and
have different ranges?
The function
is one-to-one on
thus, this interval is the range of the inverse function of
The function
is one-to-one on
thus, this interval is the range of the inverse function of
Got questions? Get instant answers now!
Why must the domain of the sine function,
be restricted to
for the inverse sine function to exist?
In order for any function to have an inverse, the function must be one-to-one and must pass the horizontal line test. The regular sine function is not one-to-one unless its domain is restricted in some way. Mathematicians have agreed to restrict the sine function to the interval
so that it is one-to-one and possesses an inverse.
Got questions? Get instant answers now!
Questions & Answers
the diagram of the digestive system
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Diversity of living thing
ISCONT
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.