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

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

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

lgbasallote
 3 years ago
Best 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?

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0no idk what you just did

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

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

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0yeah but whats beta?

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

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.1ahh we'll get there

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

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

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.1i was talking to sugarrainbow

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

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0umm 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

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

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

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

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

Skaematik
 3 years ago
Best ResponseYou've already chosen the best response.0This 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

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

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

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

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

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

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

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

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

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0how did you get 5.32

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

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

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

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

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

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

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

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

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

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

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

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0okay that makes sense

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

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

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

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

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

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

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

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

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

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

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

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.1it'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.

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.1basically 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...

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

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

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

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

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

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.1yeah, 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

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0umm 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

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

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

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

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.1you 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:)

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

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.1no, 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 :)

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0umm 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?

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

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

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.11/4 the way around a circle.

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0oh 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

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

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

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

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

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