Notes for Unit Circle (2 Viewers)

od9895

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Hello
I need your help guys. Do any you guys have notes or past exams on the unit circle because apparantly my tutor said it is compulsory to know how to use the unit circle in trig. Please help!!!

Thanks
 

Carrotsticks

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Perhaps you can use that tutor to help you get notes? That's what they're paid for after all....

Unless you want a tutor FOR your tutor, who tutors for your school.
 

deswa1

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The unit circle isn't a topic by itself so you won't find a whole exam on it. What exactly do you need help with and I'll try and come up with something :)
 

od9895

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I need help with everything on the unit circle because I am new to my tutor and I dont know anything about it
 

RealiseNothing

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Draw a unit circle (centre 0,0 on a number plane with radius 1).

Now draw 2 diagonal lines through the centre ( should look like y=x and y=-x ).

The angles these lines make with the x axis are called the related angle. The top right quadrant is the first, followed by the top left, then bottom left, and finally the bottom right being the 4th quadrant.

You should have 4 related angles, each in a different quadrant. Draw perpendicular lines straight down from the intersection of your diagonal lines and the unit circle, this will make 4 congruent right angled triangles. Let the angle made at the origin of the triangle be theta.

Now you can use sin/cos/tan to prove a few indentities for theta in each of the 4 different quadrants. Hint: Let the hypotenuse be 'r' as it is the radius of the unit circle, and then let the vertical side of the triangle be 'y' and the horizontal side be 'x'.

You will come up with a general case for sin, cos, and tan in each quadrant which you can use for any length 'r'. However since it's a unit circle and the radius is 1, let r=1 and see what happens to these identities. These new identities are special cases on a unit circle.

Using this diagram you can also derive other identities, so just play around with it a bit (see when sin/cos/tan are positive or negative).

You can also see things such as sin@ = cos(90-@) through the diagram.

Note: I did this instead of just telling you the identities as you will understand it more if you derive it yourself instead of accepting it as fact.
 

RivalryofTroll

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Why can't you just ask your tutor on how to do it?
But, RealiseNothing just explained the whole thing in a nutshell!
 

SpiralFlex

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*Reserved for posting later



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where .













(I can't use image tags for some reason, we'll just have to deal with it.)









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What we can do is re-arrange the formula like so,







So now,











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Writing (Estimated finish time -1 am)

Currently at ice-cream break
 
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Peeik

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Hey what textbook do you have? I'm sure most will have the unit circle in them.
 

SpiralFlex

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Note, I will probably be done by tomorrow so check then OP!
 

SpiralFlex

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Other variations I have seen over my time are,

Add Sugar To Coffee

All Silly Tom Cats

All Surfies To Cronulla
 

such_such

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ASTC doesn't apply to Dr. Truong. So if OP goes Truongs, forget about learning it the textbook way
 

RealiseNothing

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Graphically should be how it's learnt, and ASTC should be how it's remembered, in my opinion.
 

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