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do i just do pi/2-0.45?

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

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no idk what you just did

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

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

yeah but whats beta?

|dw:1347254638009:dw|

ahh we'll get there

already did.

answer is clearly .45

i was talking to sugarrainbow

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

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

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

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

and how come we add cos+sin?

cos(pi/2-beta) = sin beta

when i did pi/2 i got 0.5

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

|dw:1347256883382:dw|

cotangent of beta = 1/-5.32

how did you get -5.32

see beta?

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

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

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

what problem are you working on?

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

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

sure, look carefully at the sketch plz

|dw:1347257483078:dw|

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

|dw:1347257532660:dw|

opposite over hypotenuse is sine

okay that makes sense

cool:)

but now how do i get cos?

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

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

so that angle must be pi/2 - Beta

does this have anything to do with the unit circle

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

yeah, it all is the same thing..

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

|dw:1347257807464:dw|

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

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

|dw:1347258175266:dw|

|dw:1347258227158:dw|

|dw:1347258316959:dw|

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

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

pi/2 != 1

pi/2 = pi/2

ah the hypotenuse =1 you mean?

yeah

your pic is accurate

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

but what's pi/2?

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

pi/2 is 90 deg.

1/4 the way around a circle.

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

|dw:1347259786709:dw|

|dw:1347259882928:dw|

okay

still talking about first quadrant stuff at the moment..

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

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