A community for students.
Here's the question you clicked on:
 0 viewing
lilsis76
 2 years ago
Given tan theta = 2/3, where pi/2 < 0 < pi
and
csc B=2 where 0<B<pi/2
Find sin (0+B) and cos (B0)
ill draw the 3 data thingys given
lilsis76
 2 years ago
Given tan theta = 2/3, where pi/2 < 0 < pi and csc B=2 where 0<B<pi/2 Find sin (0+B) and cos (B0) ill draw the 3 data thingys given

This Question is Closed

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0based on the information i know it will be first quad.

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0oh duh haha its negative, so its going backwards right?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1350692578128:dw right?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0dang it, im going to need identities right? cuz it kinda looks like it :/

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0im trying to find the identities

surdawi
 2 years ago
Best ResponseYou've already chosen the best response.11st find theta and beta sin (0 + B) = sin 0 cos B + cos 0 sin B cos (0 – B) = cos 0 cos B + sin 0 sin B

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0UGH!!! okay im back lol okay, are these the identities I should know for finding theta and beta then? just so i save it?

surdawi
 2 years ago
Best ResponseYou've already chosen the best response.1\[\tan \theta=\frac{ 2 }{ 3 }\] \[\tan^{1} (\tan \theta)=\tan^{1} (\frac{ 2 }{ 3 })\]

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0okay so far i know: sin = 2/x cos =2/x and tan is the same 2/3

surdawi
 2 years ago
Best ResponseYou've already chosen the best response.1by the way what grade is this

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0okay hold on, this is precal. im in a community college, but im horrible at math haha

surdawi
 2 years ago
Best ResponseYou've already chosen the best response.1been a while since i been in the class anyways x is correct

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0oh really? did u graduate? and YAY okay i got the x, now will that be the theta?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0okay so the cos=3sqrt13 /26

surdawi
 2 years ago
Best ResponseYou've already chosen the best response.1right now im working on mydw:1350694287644:dw

surdawi
 2 years ago
Best ResponseYou've already chosen the best response.1can you calculate theta now

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0uh.... well the one i had or placed on here was wrong? the okay so the cos=3sqrt13 /26

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0is the 2 a regular 2, or a negative 2? since its going downward of the unit circle?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0wait im lost: i want to go back a lil to the soh cah toa cah is adj/hyp that would be 3 / sqrt13 dw:1350694753458:dw right?

surdawi
 2 years ago
Best ResponseYou've already chosen the best response.1thats the cos of thata, dont you want theta?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0yes the theta of tangent

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0wait. cos theta = the 3sqrt13 / 13

surdawi
 2 years ago
Best ResponseYou've already chosen the best response.1can i do it on a piece of paper then send it to you, im tired and want to go to sleep; yes i know its only 9:20 lol

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0lol yes you may. and thanks, im getting a headache from this too

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0alright so first we need to figure out where tan is negative. Using this circle dw:1350696636481:dw

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0these are when the functions are positive. for instance, in quadrant 1 , all function are positive

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0okay so tan would be negative in...................the cosine area

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0and also the sine , because tangent is \[\frac{sin\theta}{cos\theta}\]... so anytime either one is negative tan will be negative ... when sin and cos are both negative ,tan is positive which is this quadrantdw:1350696881960:dw

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0okay so the 2nd and 3rd piece on the left sides

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0next we use the information it gives about theta \[\pi/2<\theta<\pi\] can you mark these angles on my picture

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0so theta is less than \[\pi/2\] but greater than \[\pi\]dw:1350697010218:dw

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0this means \[\theta is in your second quadrant

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0alright so now lets solve the equation \[tan(\theta)=\frac{2}{3}\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0how would you get theta by itself

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0do you know about inverse trig functions?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0im back server was werid. let me look

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0no i dont know about the inverse trig functions unless your talkin about it being 1/tan or like the cos/sin

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0inverse function work as "cancelers" of trig functions they're usually denoted as \[arcsin,arctan,arccos\] or \[sin^{1},cos^{1}\] you know them because you know 1/tanx. I think you just didn't know what they were called

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0these cancel out the same trig function so \[arcsin(sin(x))=x\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0so what would you do in your case \[tan(\theta)=\frac{2}{3}\]

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0no we have not gone over this :/ and so the arctan one would be arctan(tan(x))= 2/3 ?

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0if you do arctan on one side you have to do it on the other =]

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.02/3arctan(tan(x))=2/3

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0ok say \[tan(x)=\frac{2}{3}\] you know to get rid of tan you have to use arctan, however if you multiply the left side by arctan, you have to multiply the right side also \[arctan(tan(x)=arctan(\frac{2}{3})\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0since arctan cancels tan you get \[x=arctan(\frac{2}{3})\]

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0your calculator should have an arctan symbol. it might be \[tan^{1}\]

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0so the tan^1 is called arctan?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0weird....okay, ya i didnt know any inverse ones i couldnt find the identities either :/ but i did tan^1(2/3) and it gave me.............33.69

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0alright where is 33.69 degrees?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0haha you really ask me degreees?? umm... i think its that 180/pi, right?

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0theta is in degrees unless you put in radians but keep it in degrees , all i'm asking is where on a circle would 33.69 degrees be( quadrant wise)

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0OH, umm... well hold on

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0well uh oh that isn't in the second quadrant we need to find an angle that is in the second quadrant with the same value as 33.69 degrees

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0should i start from 90 degrees?? dw:1350698677314:dw

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0hold on i know what you need to do just don't know why it's been a while since going through this material

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0i know you have to add pi(180 degrees) to it

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0okay, i think its mult. the ( 180/pi) i think

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0WAIT!!! to change to degrees you multiply 180 deg/ pi. but i would need the point for the other one to do it..... here is an example from my notes: pi/12(180/pi) cross reduce to>180 deg./12 = 15 degreessin15degrees =.2588

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0I really cant figure this one out... can you? or are you writingit down on paper, or looking it up online??

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1in your drawing at the very top, you say cos 7/25 did you mean cos(theta) = 7/25 ???

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1so because sin^2(x) + cos^2(x) = 1 you can find sin(theta) like so sin^2(theta) + cos^2(theta) = 1 sin^2(theta) + (7/25)^2 = 1 sin^2(theta) + 49/625 = 1 sin^2(theta) = 1  49/625 sin^2(theta) = 576/625 sin(theta) = sqrt(576/625) sin(theta) = 24/25

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1oh wait, sry sine is positive because 0 < theta < pi/2

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1so sin(theta) = 24/25

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1sin^2(B) + cos^2(B) = 1 sin^2(B) + (3/5)^2 = 1 sin^2(B) + 9/25 = 1 sin^2(B) = 1  9/25 sin^2(B) = 16/25 sin(B) = sqrt(16/25) ... sin(B) is negative for pi < B < 3pi/2 sin(B) = 4/5

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1So after those two steps, we now know these four pieces of info sin(theta) = 24/25 cos(theta) = 7/25 sin(B) = 4/5 cos(B) = 3/25 You can now use them in the identities sin(theta + B) = sin(theta)cos(B) + cos(theta)sin(B) cos(theta  B) = cos(theta)cos(B) + sin(theta)sin(B)

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0wait sin B is negative?? because..... its in the ..3rd quardinate and sin is negative and 24/25 is positive because it falls between the dw:1350700800280:dw 0 < theta < pi/2

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1yeah i fixed that error, my bad

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0wait sin B is negative?? because..... its in the ..3rd quardinate and sin is negative and 24/25 is positive because it falls between the dw:1350700800280:dw 0 < theta < pi/2

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0Sin B is negative??? because its in the 3rd quar. and that sin is negative and 24/25 is positive because it falls between the 0 < theta < pi/2

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1yeah i fixed that

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0okay, im checking my notes cuz i have writing in every direction

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.0okay, thank you, lol i have to write it neater and go over it again to get things down. thank you for helping me. ill give u a medal
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.