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SugarRainbow
Group Title
find the value of the expression if sin beta= 0.45, find cos(pi/2beta)
 2 years ago
 2 years ago
SugarRainbow Group Title
find the value of the expression if sin beta= 0.45, find cos(pi/2beta)
 2 years ago
 2 years ago

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SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
do i just do pi/20.45?
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
sin beta is 0.45...but beta is not 0.45 does that make sense?
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
\[\Large \cos (\frac \pi 2  \beta) \implies \cos \frac \pi 2 \cos \beta + \sin \frac \pi 2 \sin \beta\] are you familiar with this?
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
no idk what you just did
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
it's a trig formula \[\LARGE \cos (A  B ) \implies \cos A \cos B + \sin A \sin B\]
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
in this case, our A is pi/2 and B is beta make sense?
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
yeah but whats beta?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dw:1347254638009:dw
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
ahh we'll get there
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
already did.
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
so you get how \[\cos(\frac \pi 2  \beta) = \cos \frac \pi 2 \cos \beta + \sin \frac \pi 2 \sin \beta\]
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
answer is clearly .45
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
i was talking to sugarrainbow
 2 years ago

Skaematik Group TitleBest ResponseYou've already chosen the best response.0
Is it just not cos(pi/2  sin^1(0.45))?
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
umm kay i don't get algebraic's picture and i not sure how igbasallote's formula works if we don't know what beta is
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
it works because \[\cos \frac \pi 2 = 0\] \[\sin \frac \pi 2 = 1\]
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.1
so if you substitute you get \[\implies (0) \cos \beta + (1) \sin \beta\]
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
what about what Skaematik did? can't i just do that?
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
and how come we add cos+sin?
 2 years ago

Skaematik Group TitleBest ResponseYou've already chosen the best response.0
This is a formula that you will need to memorise. Its something that you can use to manipulate trignometric equations to find an answer cos(A−B)⟹cosAcosB+sinAsinB Therefore if you use it in this case, like lgbasallote said cos(π2−β)=cosπ/2cosβ+sinπ/2sinβ Plug these values into your calculator cosπ/2 sinπ/2 And you will find they equal to 0 and 1 Therefore cos(π2−β)=0+1*sinβ Sinβ =0.45 Therefore the answer is 0.45
 2 years ago

tanjung Group TitleBest ResponseYou've already chosen the best response.1
cos(pi/2beta) = sin beta
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
okay that makes more sense but what would the formula be if i had tangent(pi/2beta)=5.32 and i have to find cot?
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
when i did pi/2 i got 0.5
 2 years ago

tanjung Group TitleBest ResponseYou've already chosen the best response.1
tangent (pi/2beta) still in the first kuadrant, so impossible has a negative value and tangent (pi/2beta)=cotangent beta
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
okay so is that what cosine is or how do we get that
 2 years ago

tanjung Group TitleBest ResponseYou've already chosen the best response.1
maybe ur problem is if given tangent(pi/2beta)=5.32, find cot beta? cot beta = tan(pi/2beta) = 5.32
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dw:1347256883382:dw
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
cotangent of beta = 1/5.32
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
how did you get 5.32
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
see beta?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
what's the tangent? opp = 5.32 adjacent =1
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
tan(beta) = 5.32 and cot(beta) = 1/5.32
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
but how did you get that if we have sin and cos?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
what problem are you working on?
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
oh i'm sorry i was still looking at the first one
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
can we just go back to the first one cuz i still don't understand it
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
sure, look carefully at the sketch plz
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dw:1347257483078:dw
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
do you agree? sin(beta) = .45/1
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dw:1347257532660:dw
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
opposite over hypotenuse is sine
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
okay that makes sense
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
but now how do i get cos?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
now: dw:1347257619039:dw what's that new angle?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
the whole angle from the x axis to the y axis is 90 or pi/2 ....
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
so that angle must be pi/2  Beta
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
does this have anything to do with the unit circle
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
now look at the cosine of that angle: dw:1347257708887:dw
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
yeah, it all is the same thing..
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
see that triangle. one side is .45 the hypotenuse is 1 the other side, no one cares what it is!
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dw:1347257807464:dw
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
the cosine of that new angle is clearly .45 /1 .45 is adjacent, 1 is the hypotenuse.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
so cos(pi/2 Beta) is .45
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
it's what @tanjung said : cos(pi/2beta) = sin beta but I showed it graphical so you could believe! you can't really argue with that picture.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
basically if two angles are complimentary, the cosine of one angle is the sin of the other.... ie the side that is opposite on one triangle *must be* the side that is adjacent on the other triangle...
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dw:1347258175266:dw
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dw:1347258227158:dw
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dw:1347258316959:dw
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
umm okay is it also because its sin and cos that its the same?
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
real quick, since pi/2=1 then would i just divide .45(sine beta) by 1 to get cos?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
yeah, I guess I get what you're saying... it comes from the definition of sin as opp/hyp and cosine as adj/hyp when you draw those sides for two angles which are complimentary they make a rectangle
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
pi/2 != 1
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
pi/2 = pi/2
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
umm okay so thinking of it in terms of a rectangle that means cos is the same as sin because the two sides are equal?dw:1347258695721:dw
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
ah the hypotenuse =1 you mean?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
cosine isn't the same as sine.... that's not what I said, but yeah you're starting to get it, I think...
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
your pic is accurate
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
you see that, in your pic: dw:1347258903616:dw those two angles aren't the same? they do add up to give pi/2 (90 degrees) though so the cosine of one angle = the sine of the other:)
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
oh so its only the same cuz it the angle adds up to 90?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
no, it works elsewhere on the circle. but just try to grasp this 1st quadrant sketch for now... then you can move on to more advanced stuff :)
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
umm okay i do get how you got hyp=1 and opp=.45 but what bout the angles how did you get that they'd = 90?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
well remember, because if Beta is one of the angles and the other is pi/2  Beta then Beta + (pi/2  Beta) = pi/2
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
but what's pi/2?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
so we're automatically talking about two angles that add up to pi/2.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
pi/2 is 90 deg.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
1/4 the way around a circle.
 2 years ago

SugarRainbow Group TitleBest ResponseYou've already chosen the best response.0
oh i just put it in my calc and i see how you got 90 but how does that necessarily help us with this because a bunch of different combinations of angles can add up to 90
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
that's good actually. that means it works no matter what Beta is. It's general. For any Beta.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dw:1347259786709:dw
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dw:1347259882928:dw
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
still talking about first quadrant stuff at the moment..
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
anyway hope that cleared it up. think it over a bit, you'll see why it has to be true.
 2 years ago
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