# 5.6 Inverse trigonometric functions  (Page 8/15)

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The line $\text{\hspace{0.17em}}y=\frac{3}{5}x\text{\hspace{0.17em}}$ passes through the origin in the x , y -plane. What is the measure of the angle that the line makes with the positive x -axis?

The line $\text{\hspace{0.17em}}y=\frac{-3}{7}x\text{\hspace{0.17em}}$ passes through the origin in the x , y -plane. What is the measure of the angle that the line makes with the negative x -axis?

What percentage grade should a road have if the angle of elevation of the road is 4 degrees? (The percentage grade is defined as the change in the altitude of the road over a 100-foot horizontal distance. For example a 5% grade means that the road rises 5 feet for every 100 feet of horizontal distance.)

A 20-foot ladder leans up against the side of a building so that the foot of the ladder is 10 feet from the base of the building. If specifications call for the ladder's angle of elevation to be between 35 and 45 degrees, does the placement of this ladder satisfy safety specifications?

No. The angle the ladder makes with the horizontal is 60 degrees.

Suppose a 15-foot ladder leans against the side of a house so that the angle of elevation of the ladder is 42 degrees. How far is the foot of the ladder from the side of the house?

## Graphs of the Sine and Cosine Functions

For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.

$f\left(x\right)=-3\mathrm{cos}\text{\hspace{0.17em}}x+3$

amplitude: 3; period: $\text{\hspace{0.17em}}2\pi ;\text{\hspace{0.17em}}$ midline: $\text{\hspace{0.17em}}y=3;\text{\hspace{0.17em}}$ no asymptotes

$f\left(x\right)=\frac{1}{4}\mathrm{sin}\text{\hspace{0.17em}}x$

$f\left(x\right)=3\mathrm{cos}\left(x+\frac{\pi }{6}\right)$

amplitude: 3; period: $\text{\hspace{0.17em}}2\pi ;\text{\hspace{0.17em}}$ midline: $\text{\hspace{0.17em}}y=0;\text{\hspace{0.17em}}$ no asymptotes

$f\left(x\right)=-2\mathrm{sin}\left(x-\frac{2\pi }{3}\right)$

$f\left(x\right)=3\mathrm{sin}\left(x-\frac{\pi }{4}\right)-4$

amplitude: 3; period: $\text{\hspace{0.17em}}2\pi ;\text{\hspace{0.17em}}$ midline: $\text{\hspace{0.17em}}y=-4;\text{\hspace{0.17em}}$ no asymptotes

$f\left(x\right)=2\left(\mathrm{cos}\left(x-\frac{4\pi }{3}\right)+1\right)$

$f\left(x\right)=6\mathrm{sin}\left(3x-\frac{\pi }{6}\right)-1$

amplitude: 6; period: $\text{\hspace{0.17em}}\frac{2\pi }{3};\text{\hspace{0.17em}}$ midline: $\text{\hspace{0.17em}}y=-1;\text{\hspace{0.17em}}$ no asymptotes

$f\left(x\right)=-100\mathrm{sin}\left(50x-20\right)$

## Graphs of the Other Trigonometric Functions

For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.

$f\left(x\right)=\mathrm{tan}\text{\hspace{0.17em}}x-4$

stretching factor: none; period: midline: asymptotes: where is an integer

$f\left(x\right)=2\mathrm{tan}\left(x-\frac{\pi }{6}\right)$

$f\left(x\right)=-3\mathrm{tan}\left(4x\right)-2$

stretching factor: 3; period: midline: asymptotes: $x=\frac{\pi }{8}+\frac{\pi }{4}k,$ where is an integer

$f\left(x\right)=0.2\mathrm{cos}\left(0.1x\right)+0.3$

For the following exercises, graph two full periods. Identify the period, the phase shift, the amplitude, and asymptotes.

$f\left(x\right)=\frac{1}{3}\mathrm{sec}\text{\hspace{0.17em}}x$

amplitude: none; period: $2\pi ;$ no phase shift; asymptotes: where is an odd integer

$f\left(x\right)=3\mathrm{cot}\text{\hspace{0.17em}}x$

$f\left(x\right)=4\mathrm{csc}\left(5x\right)$

amplitude: none; period: no phase shift; asymptotes: where is an integer

$f\left(x\right)=8\mathrm{sec}\left(\frac{1}{4}x\right)$

$f\left(x\right)=\frac{2}{3}\mathrm{csc}\left(\frac{1}{2}x\right)$

amplitude: none; period: no phase shift; asymptotes: where is an integer

$f\left(x\right)=-\mathrm{csc}\left(2x+\pi \right)$

For the following exercises, use this scenario: The population of a city has risen and fallen over a 20-year interval. Its population may be modeled by the following function: $\text{\hspace{0.17em}}y=12,000+8,000\mathrm{sin}\left(0.628x\right),\text{\hspace{0.17em}}$ where the domain is the years since 1980 and the range is the population of the city.

What is the largest and smallest population the city may have?

largest: 20,000; smallest: 4,000

Graph the function on the domain of $\text{\hspace{0.17em}}\left[0,40\right]$ .

memory of development brain of the human psychologist
?
lord
hlo
Ananya
Haw are you?
Shilan
hi
zge
hello
Emm
usef
hi
Gil
Haw are you?
Shilan
Aha ok
Shilan
hi
Daniella
waasup
Isaiah
hello
Sara
hello
androi
Haw are you
Shilan
im ok you
Daniella
Me to
Shilan
Thanks
Shilan
What's going?
Shilan
working
Daniella
hey everyone this Mahmoud
Mahmoud
is
Mahmoud
Fine
Shilan
Hello
Jobe
how is it going people?
Tomasz
kind
Alter
thanks
Alter
hi..!
Alter
yes we'll
Alter
yes we'll
Alter
how did psychology begin?
of psychologys commencement, the traces can be seen in the work of Aristotle, where he talk about soul and body, likewise work in durrant, de anima, all these were somewhere supporting dualism, in which soul could exist separately from body
amaan
but if you talk about the moder psychology, Gustav fechner, is credited with performing scientific experiments, basis of his experiments in psychology with his studies perception.
amaan
hi, can you help me to find research related to child truma
Heba
does psychology deal with love?
Maybe, i think
edem
I definitely would say yes
Clara
how so
Isaiah
*triarchic
Meredith
there are so many different reasons why you can fall in love with someone, many of them develope subconsciously -> psychology
Clara
love messes with the brain, a lot, ergo I believe that Psychology does indeed deal with love
I would like an example as to what and how you think it deals with.
Tyler
how can I discover that this individual has a long-term memory and shot- term memory?
Namuaha
what is synapse
In the central nervous system, a synapse is a small gap at the end of a neuron that allows a signal to pass from one neuron to the next. synapse are found where nerve cells connect with other nerve cells
Najeem
a synapse the connection is where a neuron cell connects to another neuron cell.
Shaun
good
Jobe
what is psychology
Jobe
can you do auto book auto
WHT u mean?
usef
yes
MD
heyy, may i join the conversation please?
yes of course
Najeem
how to avoid theory of bias confirmation in real life
Scar
yes
Jobe
hello
Bhavin
hello to all
Genevieve
hey, may I join the conversation?
samra
salaam
Ibrahim
so i cn even do this after ba hons in psychology?
Avneet
the only eligibility criteria is that you should have 50% of aggregate in your psychology papers. (bachelors)
syeda
okay thank you so much❤ have a lovely day🙂
Avneet
you're welcome. glad it helped ^_^
syeda
To pursue a career as a psychotherapist you'll have to do your bachelors in psychology. (bsc honors is preferable). since there are many fields and you've chosen as a therapist. a masters degree in clinical psychology or therapy and family counseling is preferable.
syeda
so i cn even do this after ba hons in psychology?
Avneet
yes you can.
syeda
you're welcome. glad it helped ^_^
syeda
hello
Vhikkie
yh
Parker
hello
Avneet
is there any psychotherapist here? i need to know the qualification one hve to pursue.
Avneet
I'm clinic psychologist...
Shilan
Hey. I'm pursuing BA in Clinical Psychology
Aakarshan
the only eligibility criteria is that you should have 50% of aggregate in your psychology papers. (bachelors)
syeda
hello
Vhikkie
who is the father of psychology
aristatil
and please, how would you guys, describe the study of psychology at college ?
edem
psychologist student?
Aspen
i mean not yet but am about to start college so wanna know how is it(college in general and psychology course) please
edem
Psychology is the study of mind and behaviour. So if you will take psychology as a subject so you will get to know how your everything (physical, mental, social, spiritual aspects) effects your behaviour
sakina
With this brief knowledge you can help people to cope up with their problems and only you can guide them correctly
sakina
And if you go for further specialisations you can study hypnosis, face reading, body language etc
sakina
Thanks a lot🙏🏾 And ik some of the stuffs u said but i am also going to write thesis, right ?
edem
ok no prob, thanks a lot🙏🏾✨
edem
cerebellum
Khan
hae everyone, hope you are well this evning my question is what is the difference between drive and motivation
Michael
good question
Rainee
drive is more like an impulse or urge and i think they both go together (drive and motivation) even if there is a slight difference
edem
@ Michael Drive is delivered to be innate without the use of an external stimuli, motivation normally evolves an outside stimuli which may include praise, appreciate, or reward.
Reginald
*believed...sorry for typo
Reginald
@Reginald, can't the motivation come from the inner self?
edem
Good question, please give an example.
Reginald
can we say desire of success for example
edem
Wilhelm Wundt is the father of psychology
ipau
Wilhem Wundt thank you for the road that you opened.
Qwanta
You mean who is the father of having a great educated argumentative guess? nothing is more wrong than this question. The question is you should ask yourselfs is, how sure are you abour their scientific studying? one's percieved assimilated approach to judging another person and saying they are
Roger
the biggest problem with scientific research and data is that ya you could get the same result 1000 times then it could go the other way 1000 times, but we would never know that and we did, we would still say ya but the proof is there. The only thing science proves is that humanity has
Roger
no facts about human behavior in the scientific context, but more in the trial and error.. sorry to tell you, but so far no one has proven Father of anything, thats up to you and i, judgement is bias, science is good enough lazy
Roger
cognitive development is the growing and development of the brain.
Ecofascism is a theoretical political model in which an authoritarian government would require individuals to sacrifice their own interests to the "organic whole of nature". The term is also used as a rhetorical pejorative to undermine the environmental movement.
ipau
what's the big difference between prejudice and discrimination?
A prejudiced person may not act on their attitude.  Therefore, someone can be prejudiced towards a certain group but not discriminate against them.  Also, prejudice includes all three components of an attitude (affective, behavioral and cognitive), whereas discrimination just involves behavior
Nancy Lee
hi
basher
hello
Rahul
what is all about cognitive development?
Kamohelo
cognitive development is the growing and development of the brain
Jessy
how do you control a variable when using spss whilst running a pearsons correlation analysis?
it dependa on your study. according to what you want to say and explain your result
Pouran
Hello
Jobe
why does it say her and she
stages of cognitive development
sensory preoperatinal concrete formal
Rajendra
What's mental memory?
Namuaha
Memory is our ability to encode, store, retain and subsequently recall information and past experiences in the human brain. It can be thought of in general terms as the use of past experience to affect or influence current behaviour.
Shilan
What I mental memory?
Namuaha
What's mental memory?
Namuaha
my thankful
Namuaha
Jobe
what is psychology
the study of insecurities and the effect on the host .
Sera
Psychology is the scientific study of behavior & mental processes
Angela
psychology is science about learning human behaviour
Zhamshid
behaviorosm
Khan
is the study of human behaviour and mental processes
Jobe
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