Question

Pre-cal 12 Question!

About: Unit circle


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Answer 1

I understand that it is in Quadrant 3. How do we find the coordinates.

Answer 2

P(theta)= (x,y) point that lies on the unit circle.

Answer 3

yes

Answer 4

90 degrees to that line, you swap the x,y coords, and negate one of them
in other words, if you start with (x,y), then both (-y,x) and (y,-x) are "turned" 90 degrees i.e. pi/2 radians
I would plot both points and then it should be clear which is rotated +pi/2 i.e. counter-clockwise and which is - pi/w (clockwise)

Answer 5

ok

Answer 6

for example, if you started with (1,0 )
then (-0, 1) or just (0,1)
and
(0,-1) are both points rotated 90 degrees.

Answer 7

right

Answer 8

in your problem, swap the two coords
then negate the "new" x value and plot it. where is it ?

Answer 9

Do you mean adding and substracting the 90 degrees?

Answer 10

Yes, I am saying if we know (x,y) for P(theta)
then P(theta+pi/2) is (-y,x)

Answer 11

ok

Answer 12

But I figured out a new method. Using sine and sin^-1

If use sine^-1 of the coordinate, it will give us the angle.

Ex.
Sine^-1 (-2squareroot 2/3) we get -70.5 degrees

Answer 13

Now if we add 90 + 70.5 it will give us 160.5. Sine(160.5) will give us 1/3 for the y-coordiate. Assume it is negative because it is in quadrant 3. Is this correct?

Answer 14

70.5 is the "reference angle". the actual angle is 180+70.5 = 250.5
now add 90 to get 340.5 (notice you are in the correct quadrant, Q IV)
now you can do cos and sin to find the x and y values of the coord.

Answer 15

ok

Answer 16

But you need a calculator to do that, and it may not be obvious what the *exact* values are
i.e. the 2*sqr(2)/3 for the x value

Answer 17

if you know the sum of angle formulas, you can do this

P is at (x,y) and it has angle A (we know A is about 250.5, but for now assume we don't know it).
we also know that x is cos A, and y is sin A (we are on the unit circle)
then P(A+90) has coords cos(A+90), sin(A+90
expand cos(A+90)= cos A cos 90 - sin A sin 90 = - sin A (remember cos 90 is 0)
and sin(A+90)= sin A cos 90 + cos A sin 90 = cos A
thus the coords are -sin A, cos A
or knowing x is cos A and y is sin A, (-y,x)
in terms of the coords of P

Answer 18

Ok, I have a question

Answer 19

If we face a situation like this, finding the reference angle and then the central angle and then central angle + 90 degrees. Is this the best method? I was absent in the class, and I do not know which method my teacher thaught students to solve this. So what do you think?

Answer 20

I figured this method out, it works in all situations

Answer 21

with special angles like 90, I would do as I posted, using sum of angle formulas
but for 90 degrees I would use (x,y) --> (-y, x) ccw and (y,-x) clockwise

Generally, though your idea is good, it would not be used on a test. They probably want you to learn the sum of angles idea.

Answer 22

Or maybe they want you to learn the "swap x and y" trick. It is useful in coordinate geometry and in calculus

Answer 23

Ok I see.

Answer 24

Thank you for your method, I am going to review it again, If I had any other questions I will tag you back in this question.Thanks for your time.