Stephanie's Reflection

1)s=rθ
2)k=1/2r^2θ (k=1/2rs)
r = radius, θ = angle, s = arc length, k = area of sector

EG: A sector of a circle has an arc length of 6cm and an area of 75cm^2. Find its radius and measure of its central angle.
s=6cm
k=75cm^2
r=?
θ=?
k=1/2rs
75=1/2r6
75=3r
r=25cm
s=r
6=25θ
θ=6/25

sinθ=y/r
cosθ=x/r
tanθ=y/x
cscθ=r/x
secθ=x/y
cotθ=x/y
r=√(x^2+y^2)

EG: sin180° = y/r
at 180°, y=0
0/1 = 0
thus sin180°=0

EG: cosπ/2 = x/r
π/2 is at 90°
at 90°, x=0
thus cosπ/2=0

Trig Chart:
0°
sin0=0
cos0=1
tan0=0
csc0=undefined
sec0=1
cot0=0
30°
sinπ/6=1/2
cosπ/6=√3/2
tanπ/6=√3/3
cscπ/6=2
secπ/6=2 √3/3
cotπ/6=√3
45°
sinπ/4=√2/2
cosπ/4=√2/2
tanπ/4=1
cscπ/4=√2
secπ/4=√2
cotπ/4=1
60°
sinπ/3=√3/2
cosπ/3=1/2
tanπ/3=√3
cscπ/3=2 √3/3
secπ/3=2
cotπ/3=√3/2
90°
sinπ/2=1
cosπ/2=0
tanπ/2=undefined
cscπ/2=1
secπ/2=undefined
cotπ/2=0

Reference Angles (must be between 0° and 90°)
1)find which quadrant angle is in
2)determine the sign in that quadrant (+ve or -ve)
3)subtract 180° until the angle is between 0° and 90° (0 and π/2)

1)find the reference angle using chart or calculator
2)find what quadrant you need to be in based on the sign of the value
3)use notes to move to that quadrant
To Move:
I to IV = make negative and add 360°
I to III = add 180°
I to II = make negative and add 180°
II to IV = add 180°

EG: sin^-1(-√2/2) = 45°
45 + 180 = 225° = θ
I to IV
-45 + 360 = 315°
θ = 225°, 315°

I believe I mostly caught up with this stuff but I still don't quite understand the last few sections.