Find sin x and csc y
First of all how do use csc on a calculator (if possible)
of all how in the world do I set up the equations to solve?
I know that sin is opposite over hypotenuse and csc is hypotenuse over opposite

- cutiecomittee123

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- cutiecomittee123

|dw:1441828737649:dw|

- Nnesha

csc is reciprocal of 1/sin
sec is reciprocal of 1/cos
cot is reciprocal of 1/tan

- cutiecomittee123

makes sense. so then to solve for sinx
sinx=5/a

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## More answers

- cutiecomittee123

right?

- Nnesha

first ) apply the Pythagorean theorem to find 3rd side of right triangle \[\huge\rm a^2+b^2=c^2\]

- Nnesha

yes right but first find c (hypotenuse )
let hypotenuse = c

- cutiecomittee123

okay so 25+49=74

- cutiecomittee123

and the sqrt of 74 is the hypotenuse

- Nnesha

yes right that is c^2 but we need c

- Nnesha

yes right

- Nnesha

\(\color{blue}{\text{Originally Posted by}}\) @cutiecomittee123
makes sense. so then to solve for sinx
sinx=5/a
\(\color{blue}{\text{End of Quote}}\)
now substitute a for sqrt{74}

- cutiecomittee123

which is 8.6

- cutiecomittee123

do i keep it
sin(x)=5/sqrt74
or do i simplify

- cutiecomittee123

okay

- Nnesha

yes simplify solve for x

- cutiecomittee123

i get a crazy weird number when i try to calculate that

- Nnesha

what did you get ? first of all your calculator mode should be on degree
2nd you should take invs sin

- Nnesha

understand ? ?//

- cutiecomittee123

okay hold on

- cutiecomittee123

i get sinx=.0011792563

- Nnesha

when we have to find an angle then we should use `invs sin` \[x = \sin^{-1} \frac{ 5 }{ 8.6 }\]

- Nnesha

or in other words `arcsin` http://prntscr.com/8eiznl

- cutiecomittee123

okay so you just keep it that way, no more simplifying?

- Nnesha

no use calculator to find x \[x = \sin^{-1} \frac{ 5 }{ 8.6 }\]

- cutiecomittee123

alright so x=8.6

- cutiecomittee123

@Nnesha

- Nnesha

hmm not x isn't 8.6
the hypotenuse = 8.6

- Nnesha

|dw:1441834691882:dw|

- Nnesha

type this into the calculator \[ \sin^{-1} \frac{ 5 }{ 8.6 }\]

- cutiecomittee123

I did

- cutiecomittee123

it gave me 8.6

- cutiecomittee123

wait no it gives me .0011792563

- Nnesha

hmm not sure how u got that
what did you type into the calculator ?

- cutiecomittee123

i typed x^-1 before then sin(5/8.6)

- Nnesha

it's sin^{-1} not x^{-1}
arcsin =sin^{-1}

- cutiecomittee123

okay so 98.55

- cutiecomittee123

that is what i get when i put the inverse second after the other part of the equation

- Nnesha

on ti-84 calculator ?

- cutiecomittee123

yeah

- cutiecomittee123

x^-1 is inverse

- Nnesha

for that calculator press `2nd-sin` then type (5/8.6)

- cutiecomittee123

Ahh I see, way more acurate answer.
x=35.55

- Nnesha

got it !

- Nnesha

that's right !

- cutiecomittee123

okay and then we have to find the csc of y, an you help

- cutiecomittee123

can*

- Nnesha

i'll use the fact that all triangles add up to 180 degree
so it's right triangle so one angle 90 other angle we just found 35.5
i don't knw why sin (x)= 8.6/7 gives me error on calculator

- cutiecomittee123

y=54.5

- Nnesha

yes right

- cutiecomittee123

alright, i dont know if you still want to help but there are two more and i think i have the hang of it, but it is always nice to have a little help:)
find tan c and cot y
and
find cos x and sec y

- Nnesha

geez i don't know why it csc y giving me an error
anyways \[\huge\rm csc( x )=\frac{ 8.6 }{ 7 }\] then find inverse csc

- cutiecomittee123

there is no csc button

- Nnesha

with same triangle ?

- Nnesha

i know but csc = 1/sin
so it should be i /sin^{-1}(7/8.6)

- cutiecomittee123

yes same triangle
Okay let me try that

- cutiecomittee123

so plug in
1/sin(-1) (7/8.6) ????

- Nnesha

welll i plugged in sin^{-1} (7/8.6) i got 54.48

- Nnesha

still don't understand anyways move to the next one

- cutiecomittee123

waiiiiittt, are we still working on the first problem to find
csc(y)? because i got the same answer
y=54.5 because i just used your advice that there are 180 degrees in a triangle and we already have 90+35.5 and then i subtracted them from 180 and got 54.5 as well. I think that is the right answer

- Nnesha

yes that's the right answer but i was trying to find how to find csc y without using the fact 180 degree :D

- Nnesha

\(\color{blue}{\text{Originally Posted by}}\) @cutiecomittee123
alright, i dont know if you still want to help but there are two more and i think i have the hang of it, but it is always nice to have a little help:)
find `tan c` and cot y
and
find cos x and sec y
\(\color{blue}{\text{End of Quote}}\)
do you mean `tan x` ???

- cutiecomittee123

yes tan x

- Nnesha

alright try it first
remember cot is reciprocal of tan

- cutiecomittee123

well tan(x)=5/7

- Nnesha

right solve for x !

- cutiecomittee123

Okay so I would just multiply by 7 on each side and that makes it
7tan(x)=35

- Nnesha

well you don't have to multiply by 7
just take the invs tan and then calculator

- cutiecomittee123

okay so i did 2nd, tan(5/7) and i got 35.54

- Nnesha

perfect!

- cutiecomittee123

i did it? is that it lol

- Nnesha

yes right that's tan x

- cutiecomittee123

okay so now to find cot y

- cutiecomittee123

wouldnt it just be cot y = 7/5

- cutiecomittee123

oh is it just tan(5/7)

- Nnesha

tan y = what ?

- cutiecomittee123

well it is inverse tan so i figured you use tan when calculating

- Nnesha

well you did the opposite
tan = opposite over adjacent
and cot = adjacent over opposite

- cutiecomittee123

so you keep it the way it is but just dont take the iverse? sine we took the inverse to find tan x

- cutiecomittee123

inverse
since *

- Nnesha

guess what i'm so hungry right now
i need 2nd opinion on this one
i feel like we don't need angle
we just write in the form tan x = 7/5 that's it

- Nnesha

is it just find sin x or solve for x ?

- Nnesha

or like what is x and y ?

- Nnesha

\(\color{blue}{\text{Originally Posted by}}\) @cutiecomittee123
wouldnt it just be cot y = 7/5
\(\color{blue}{\text{End of Quote}}\)
cot y = 5/7 ( adjacent over opposite)
so it would be arctan(7/5)

- Nnesha

ye then cos = adjacent over hyp
so same concept with sec just like cot
i think ur afk

- Nnesha

i've to go now.

- cutiecomittee123

okay i see. Thanks for your help!!!

- Nnesha

yw

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