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find the value of the expression if sin beta= 0.45, find cos(pi/2beta)
 one year ago
 one year ago
find the value of the expression if sin beta= 0.45, find cos(pi/2beta)
 one year ago
 one year ago

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SugarRainbowBest ResponseYou've already chosen the best response.0
do i just do pi/20.45?
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
sin beta is 0.45...but beta is not 0.45 does that make sense?
 one year ago

lgbasalloteBest 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?
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
no idk what you just did
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
it's a trig formula \[\LARGE \cos (A  B ) \implies \cos A \cos B + \sin A \sin B\]
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
in this case, our A is pi/2 and B is beta make sense?
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
yeah but whats beta?
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
dw:1347254638009:dw
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
ahh we'll get there
 one year ago

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

Algebraic!Best ResponseYou've already chosen the best response.1
answer is clearly .45
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
i was talking to sugarrainbow
 one year ago

SkaematikBest ResponseYou've already chosen the best response.0
Is it just not cos(pi/2  sin^1(0.45))?
 one year ago

SugarRainbowBest 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
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
it works because \[\cos \frac \pi 2 = 0\] \[\sin \frac \pi 2 = 1\]
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.1
so if you substitute you get \[\implies (0) \cos \beta + (1) \sin \beta\]
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
what about what Skaematik did? can't i just do that?
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
and how come we add cos+sin?
 one year ago

SkaematikBest 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
 one year ago

tanjungBest ResponseYou've already chosen the best response.1
cos(pi/2beta) = sin beta
 one year ago

SugarRainbowBest 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?
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
when i did pi/2 i got 0.5
 one year ago

tanjungBest 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
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
okay so is that what cosine is or how do we get that
 one year ago

tanjungBest 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
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
dw:1347256883382:dw
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
cotangent of beta = 1/5.32
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
how did you get 5.32
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
what's the tangent? opp = 5.32 adjacent =1
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
tan(beta) = 5.32 and cot(beta) = 1/5.32
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
but how did you get that if we have sin and cos?
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
what problem are you working on?
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
oh i'm sorry i was still looking at the first one
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
can we just go back to the first one cuz i still don't understand it
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
sure, look carefully at the sketch plz
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
dw:1347257483078:dw
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
do you agree? sin(beta) = .45/1
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
dw:1347257532660:dw
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
opposite over hypotenuse is sine
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
okay that makes sense
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
but now how do i get cos?
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
now: dw:1347257619039:dw what's that new angle?
 one year ago

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

Algebraic!Best ResponseYou've already chosen the best response.1
so that angle must be pi/2  Beta
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
does this have anything to do with the unit circle
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
now look at the cosine of that angle: dw:1347257708887:dw
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
yeah, it all is the same thing..
 one year ago

Algebraic!Best 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!
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
dw:1347257807464:dw
 one year ago

Algebraic!Best 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.
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
so cos(pi/2 Beta) is .45
 one year ago

Algebraic!Best 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.
 one year ago

Algebraic!Best 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...
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
dw:1347258175266:dw
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
dw:1347258227158:dw
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
dw:1347258316959:dw
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
umm okay is it also because its sin and cos that its the same?
 one year ago

SugarRainbowBest 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?
 one year ago

Algebraic!Best 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
 one year ago

SugarRainbowBest 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
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
ah the hypotenuse =1 you mean?
 one year ago

Algebraic!Best 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...
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
your pic is accurate
 one year ago

Algebraic!Best 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:)
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
oh so its only the same cuz it the angle adds up to 90?
 one year ago

Algebraic!Best 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 :)
 one year ago

SugarRainbowBest 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?
 one year ago

Algebraic!Best 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
 one year ago

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

Algebraic!Best ResponseYou've already chosen the best response.1
1/4 the way around a circle.
 one year ago

SugarRainbowBest 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
 one year ago

Algebraic!Best 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.
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
dw:1347259786709:dw
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
dw:1347259882928:dw
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.1
still talking about first quadrant stuff at the moment..
 one year ago

Algebraic!Best 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.
 one year ago
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