Unit circle?

Question

I'm taking Algebra 2 w/Trig. We got a copy of the unit circle, and we have to memorize it. I've been sick over Thanksgiving break, and have not finished learning it. Any tips to help me remember it. Thanks!

Answer 1

use symmetry,
sin(-a) = -sin(a) means that the y- coordinate of y has the same length as the y-coordinate of -a

In an analogue way for cos(a)=-cos(a) but this time you have the x-coordinate.

Also I use the following trick
sin(pi/6) is the smallest of sqrt(3)/2 and 1/2
cos(pi/6)is the biggest of sqrt(3)/2 and 1/2

now switch because pi/3 is bigger than pi/6:

sin(pi/3) is the biggest of sqrt(3)/2 and 1/2
cos(pi/3)is the smallest of sqrt(3)/2 and 1/2

Answer 2

The denominators for the fractions are the same: pi/6 is closest to the x-axis, pi/3 is closest to the y-axis, pi/4 is in the middle.

For the numerators:
2nd quadrant= numerator is 1 less than denominator (d-1=n)
3rd quadrant= numerator is 1 more than denominator (d+1=n)
4th quadrant= just remember 5-7-11?

OR

It's a phone number: 235-754-5711 (the 11 is eleven, really)

Other than that, it's just the four points, which you should be able to memorize.

Answer 3

Consider rotating vector of radius r centre O which makes an angle θ with x axis:-

cos θ = x/r
sin θ = y/r
tan θ = y/x

1st Quadrant
All are positive

2nd Quadrant
Only sin θ is positive

3rd Quadrant
Only tan θ is positive

4th Quadrant
Only cos θ is positive

Which leads to :-

sin | All
----------
tan | cos

If circle is of unit radius, r = 1

Answer 4

the easy way i do is just see the trend on those unit circle. the same length on x and y has the same values on its trig. the x values negative cause the tan and cos negative, the y negative cause the tan and sine negative
if both x n y are negative sine and cos are negative