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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
 one year ago
 one year 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
 one year ago
 one year ago

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lilsis76Best ResponseYou've already chosen the best response.0
dw:1350692195063:dw
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
based on the information i know it will be first quad.
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
oh duh haha its negative, so its going backwards right?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
dw:1350692578128:dw right?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
dang it, im going to need identities right? cuz it kinda looks like it :/
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
im trying to find the identities
 one year ago

surdawiBest ResponseYou've already chosen the best response.1
1st 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
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
UGH!!! okay im back lol okay, are these the identities I should know for finding theta and beta then? just so i save it?
 one year ago

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

lilsis76Best ResponseYou've already chosen the best response.0
okay so far i know: sin = 2/x cos =2/x and tan is the same 2/3
 one year ago

surdawiBest ResponseYou've already chosen the best response.1
by the way what grade is this
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay hold on, this is precal. im in a community college, but im horrible at math haha
 one year ago

surdawiBest ResponseYou've already chosen the best response.1
been a while since i been in the class anyways x is correct
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
oh really? did u graduate? and YAY okay i got the x, now will that be the theta?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay so the cos=3sqrt13 /26
 one year ago

surdawiBest ResponseYou've already chosen the best response.1
right now im working on mydw:1350694287644:dw
 one year ago

surdawiBest ResponseYou've already chosen the best response.1
can you calculate theta now
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
uh.... well the one i had or placed on here was wrong? the okay so the cos=3sqrt13 /26
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
is the 2 a regular 2, or a negative 2? since its going downward of the unit circle?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
wait 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?
 one year ago

surdawiBest ResponseYou've already chosen the best response.1
thats the cos of thata, dont you want theta?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
yes the theta of tangent
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
wait. cos theta = the 3sqrt13 / 13
 one year ago

surdawiBest ResponseYou've already chosen the best response.1
can 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
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
lol yes you may. and thanks, im getting a headache from this too
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
alright so first we need to figure out where tan is negative. Using this circle dw:1350696636481:dw
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
these are when the functions are positive. for instance, in quadrant 1 , all function are positive
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay so tan would be negative in...................the cosine area
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
and 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
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay so the 2nd and 3rd piece on the left sides
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
next we use the information it gives about theta \[\pi/2<\theta<\pi\] can you mark these angles on my picture
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
dw:1350697001280:dw
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
so theta is less than \[\pi/2\] but greater than \[\pi\]dw:1350697010218:dw
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
this means \[\theta is in your second quadrant
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
alright so now lets solve the equation \[tan(\theta)=\frac{2}{3}\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
how would you get theta by itself
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
do you know about inverse trig functions?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
im back server was werid. let me look
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
no i dont know about the inverse trig functions unless your talkin about it being 1/tan or like the cos/sin
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
inverse 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
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
these cancel out the same trig function so \[arcsin(sin(x))=x\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
so what would you do in your case \[tan(\theta)=\frac{2}{3}\]
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
no we have not gone over this :/ and so the arctan one would be arctan(tan(x))= 2/3 ?
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
if you do arctan on one side you have to do it on the other =]
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
2/3arctan(tan(x))=2/3
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
ok 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 \[arctan(tan(x)=arctan(\frac{2}{3})\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
since arctan cancels tan you get \[x=arctan(\frac{2}{3})\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
your calculator should have an arctan symbol. it might be \[tan^{1}\]
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
so the tan^1 is called arctan?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
weird....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
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
alright where is 33.69 degrees?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
haha you really ask me degreees?? umm... i think its that 180/pi, right?
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
theta 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)
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
OH, umm... well hold on
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
dw:1350698454198:dw
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
well 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
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
should i start from 90 degrees?? dw:1350698677314:dw
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
hold on i know what you need to do just don't know why it's been a while since going through this material
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
i know you have to add pi(180 degrees) to it
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay, i think its mult. the ( 180/pi) i think
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
WAIT!!! 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
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
I really cant figure this one out... can you? or are you writingit down on paper, or looking it up online??
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
in your drawing at the very top, you say cos 7/25 did you mean cos(theta) = 7/25 ???
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
so 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
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
oh wait, sry sine is positive because 0 < theta < pi/2
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
so sin(theta) = 24/25
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
sin^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
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
So 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)
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
wait 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
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
yeah i fixed that error, my bad
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
wait 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
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
Sin 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
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
yeah i fixed that
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay, im checking my notes cuz i have writing in every direction
 one year ago

lilsis76Best ResponseYou've already chosen the best response.0
okay, 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
 one year ago
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