Unit Q: Blogpost for concepts 2-3

tanx = rad3 / 3; cosx = -rad3 / 2
Special right triangles apply here.
Understand that:
tan = y/x
cos = x/r

when tan = rad3 / 3, the angle is 30 degrees.
when cos = - rad3 / 2, the angle is 30 degrees.



Now that we understand this, we have to find the value of the ratio when the angle is 30 degrees, so we must see that the point on the unit circle will be (rad3/2,1/2). We use this for all of the ratios.

Understand this next:
sin=y/r=1/2
csc=r/y=2
sec=r/x=2rad3/3
cot=x/y=rad3


Now that we are this far, we must remember that the angle could be in multiple quadrants. Tangent is positive so we automatically know it could be in the first or 3rd quadrant. Cosine is negative, it could be in the 2nd or 3rd quadrant. They both have the 3rd quadrant in common, so it has to be there.

sin = -1/2
csc = -2
sec = - 2rad3 / 3
cot = rad3

Using identities to solve the same problem.

We must understand all this:
sin^2 = 1 - cos^2
sin^2= 1 - (-rad3/2)^2
sin^2 = 1 - 3/4
sin^2= 1/4
rad sin^2 = rad1/4
sin = 1/2 or -1/2

csc = 1/sin
csc = 1/ (1/2)
csc = 2

sec = 1/cos
sec = 1/(-rad3/2)
sec = -2 / rad3
AT THIS STEP WE RATIONALIZE
sec = -2rad3 / 3

cot = 1/tan
cot = 1/√3/3
cot = 3/√3
RATIONALIZE THE DENOMINATOR
cot = 3rad3/3
cot = rad3