Question

Simplify the expression.

quantity cosecant of y plus cotangent of y times quantity cosecant of y minus cotangent of y divided by cosecant of y.

Answer 1

Do you know how to translate this into mathematical symbols?

Answer 2

plz start by writing them out in equation form

Answer 3

no I don't how do I do that on here?

Answer 4

u can type it like cos(y) n such...

Answer 5

plus means +
minus means -
divided by means /

Answer 6

Be sure to put the top of that division in ( ) and also the bottom in ( )

Answer 7

(csc(y)+cot(y))(csc(y)-cot(y))/(csc(y))

Answer 8

does (cscy+coty) and (cscy-coty) cancel out and leave me with the denominator?

Answer 9

Multiply the top out.
(a+b)(a-b)=a^2-b^2

Answer 10

(csc(y)^2)-(cot(y)^2)

Answer 11

good. now you should realize you could use a Pythagorean identity here

Answer 12

\[\ \text{ Recall } 1+\cot^2(y)=\csc^2(y)\]

Answer 13

yes csc2 θ = cot^2 θ=1

Answer 14

I think you mean + not = between the cot^2(theta) and 1 part.

Answer 15

whoops +1 not -1
so the cot^2 y's both cancel out and leave me with 1?

Answer 16

yes I did mean to put the + there instead

Answer 17

yes so that would mean we have 1 on top

Answer 18

and csc(y) on the bottom?

Answer 19

we have that on bottom yes

Answer 20

what is the reciprocal of csc(y)?

Answer 21

ohhhhh i see so the final answer is sin(y)?

Answer 22

yep

Answer 23

awesome! would you mind helping me with one or two more?

Answer 24

one more

Answer 25

(cos^2θ)/(sin^2θ) +cscθ sinθ

Answer 26

so remember csc(theta) is the reciprocal of sin(theta)
so csc(theta)*sin(theta)=?

Answer 27

1?

Answer 28

yep

Answer 29

now for the cos/sin part

Answer 30

cos/sin equals what trig function?

Answer 31

cot(y)

Answer 32

and yes since we have those items were squared then we have cot^2(y)

Answer 33

so we have cot^2(y)+1

Answer 34

refer back to that Pythagorean identity

Answer 35

and that is equal to csc^2θ

Answer 36

yep

Answer 37

thank you so much. I have a question for you- is ap stat anything like pre calculus? because I want to take that class next year but I am not that good at precalc

Answer 38

is ap stat a college thing? there could be some calculus in some initial stat courses but i think a lot of calculus occurs in deeper statistics

Answer 39

it is but at my high school i can take it as a senior. and okay that is really good to know. So there is a chance that someone could really stink at calculus but be good at ap stat. because I have always been very good at math but precalc is just not my forte

Answer 40

You should ask the teacher who will be teaching that course. I'm no way familiar with your course information at your school.

Answer 41

okay thank you for the help on the problems and the information!! You are amazing!

Answer 42

Glad I can help.