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
Since the functions
and
are inverse functions, why is
not equal to
Explain the meaning of
is the radian measure of an angle between
and
whose sine is 0.5.
Most calculators do not have a key to evaluate
Explain how this can be done using the cosine function or the inverse cosine function.
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.
software engineering is a the branch of computer science deals with the design,development, testing and maintenance of software applications.
Hayder
who is best bw software engineering and cyber security
Ahmad
Both software engineering and cybersecurity offer exciting career prospects, but your choice ultimately depends on your interests and skills. If you enjoy problem-solving, programming, and designing software syste
Software engineering is a branch of computer science directed to writing programs to develop Softwares that can drive or enable the functionality of some hardwares like phone , automobile and others
kelvin
if any requirement engineer is gathering requirements from client and after getting he/she Analyze them this process is called
The following text is encoded in base 64.
Ik5ldmVyIHRydXN0IGEgY29tcHV0ZXIgeW91IGNhbid0IHRocm93IG91dCBhIHdpbmRvdyIgLSBTdGV2ZSBXb3puaWFr
Decode it, and paste the decoded text here