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

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- anonymous

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

- schrodinger

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- anonymous

do i just do pi/2-0.45?

- lgbasallote

sin beta is 0.45...but beta is not 0.45 does that make sense?

- lgbasallote

\[\Large \cos (\frac \pi 2 - \beta) \implies \cos \frac \pi 2 \cos \beta + \sin \frac \pi 2 \sin \beta\]
are you familiar with this?

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## More answers

- anonymous

no idk what you just did

- lgbasallote

it's a trig formula \[\LARGE \cos (A - B ) \implies \cos A \cos B + \sin A \sin B\]

- lgbasallote

in this case, our A is pi/2 and B is beta
make sense?

- anonymous

yeah but whats beta?

- anonymous

|dw:1347254638009:dw|

- lgbasallote

ahh we'll get there

- anonymous

already did.

- lgbasallote

so you get how \[\cos(\frac \pi 2 - \beta) = \cos \frac \pi 2 \cos \beta + \sin \frac \pi 2 \sin \beta\]

- anonymous

answer is clearly .45

- lgbasallote

i was talking to sugarrainbow

- anonymous

Is it just not cos(pi/2 - sin^-1(0.45))?

- anonymous

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

- lgbasallote

it works because \[\cos \frac \pi 2 = 0\]
\[\sin \frac \pi 2 = 1\]

- lgbasallote

so if you substitute you get \[\implies (0) \cos \beta + (1) \sin \beta\]

- anonymous

what about what Skaematik did? can't i just do that?

- anonymous

and how come we add cos+sin?

- anonymous

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(Aâˆ’B)âŸ¹cosAcosB+sinAsinB
Therefore if you use it in this case, like lgbasallote said
cos(Ï€2âˆ’Î²)=cosÏ€/2cosÎ²+sinÏ€/2sinÎ²
Plug these values into your calculator
cosÏ€/2
sinÏ€/2
And you will find they equal to 0 and 1
Therefore cos(Ï€2âˆ’Î²)=0+1*sinÎ²
SinÎ² =0.45
Therefore the answer is 0.45

- anonymous

cos(pi/2-beta) = sin beta

- anonymous

okay that makes more sense but what would the formula be if i had tangent(pi/2-beta)=-5.32 and i have to find cot?

- anonymous

when i did pi/2 i got 0.5

- anonymous

tangent (pi/2-beta) still in the first kuadrant, so impossible has a negative value and tangent (pi/2-beta)=cotangent beta

- anonymous

okay so is that what cosine is or how do we get that

- anonymous

maybe ur problem is if given tangent(pi/2-beta)=5.32, find cot beta?
cot beta = tan(pi/2-beta) = 5.32

- anonymous

|dw:1347256883382:dw|

- anonymous

cotangent of beta = 1/-5.32

- anonymous

how did you get -5.32

- anonymous

see beta?

- anonymous

what's the tangent? opp = -5.32 adjacent =1

- anonymous

tan(beta) = -5.32
and
cot(beta) = 1/-5.32

- anonymous

but how did you get that if we have sin and cos?

- anonymous

what problem are you working on?

- anonymous

oh i'm sorry i was still looking at the first one

- anonymous

can we just go back to the first one cuz i still don't understand it

- anonymous

sure, look carefully at the sketch plz

- anonymous

|dw:1347257483078:dw|

- anonymous

do you agree? sin(beta) = .45/1

- anonymous

|dw:1347257532660:dw|

- anonymous

opposite over hypotenuse is sine

- anonymous

okay that makes sense

- anonymous

cool:)

- anonymous

but now how do i get cos?

- anonymous

now:
|dw:1347257619039:dw|
what's that new angle?

- anonymous

the whole angle from the x axis to the y axis is 90 or pi/2 ....

- anonymous

so that angle must be pi/2 - Beta

- anonymous

does this have anything to do with the unit circle

- anonymous

now look at the cosine of that angle:
|dw:1347257708887:dw|

- anonymous

yeah, it all is the same thing..

- anonymous

see that triangle. one side is .45 the hypotenuse is 1 the other side, no one cares what it is!

- anonymous

|dw:1347257807464:dw|

- anonymous

the cosine of that new angle is clearly .45 /1 .45 is adjacent, 1 is the hypotenuse.

- anonymous

so cos(pi/2 -Beta) is .45

- anonymous

it's what @tanjung said :
cos(pi/2-beta) = sin beta
but I showed it graphical so you could believe!
you can't really argue with that picture.

- anonymous

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...

- anonymous

|dw:1347258175266:dw|

- anonymous

|dw:1347258227158:dw|

- anonymous

|dw:1347258316959:dw|

- anonymous

umm okay is it also because its sin and cos that its the same?

- anonymous

real quick, since pi/2=1 then would i just divide .45(sine beta) by 1 to get cos?

- anonymous

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

- anonymous

pi/2 != 1

- anonymous

pi/2 = pi/2

- anonymous

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|

- anonymous

ah the hypotenuse =1 you mean?

- anonymous

yeah

- anonymous

cosine isn't the same as sine.... that's not what I said, but yeah you're starting to get it, I think...

- anonymous

your pic is accurate

- anonymous

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:)

- anonymous

oh so its only the same cuz it the angle adds up to 90?

- anonymous

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 :)

- anonymous

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?

- anonymous

well remember, because if Beta is one of the angles and the other is pi/2 - Beta then Beta + (pi/2 - Beta) = pi/2

- anonymous

but what's pi/2?

- anonymous

so we're automatically talking about two angles that add up to pi/2.

- anonymous

pi/2 is 90 deg.

- anonymous

1/4 the way around a circle.

- anonymous

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

- anonymous

that's good actually. that means it works no matter what Beta is. It's general. For any Beta.

- anonymous

|dw:1347259786709:dw|

- anonymous

|dw:1347259882928:dw|

- anonymous

okay

- anonymous

still talking about first quadrant stuff at the moment..

- anonymous

anyway hope that cleared it up. think it over a bit, you'll see why it has to be true.

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