Precalc trig (unit circle)
pi/4 (45 degrees)
(√2/2, √2/2)
pi/6 (30 degrees)
(√3/2, 1/2)
Unit circle axis labels from right counter clockwise
0pi (0 deg), 1pi/2 (90 deg), pi (180 deg), 3pi/2 (270 deg), 2pi (360 deg)
Radius of unit circle
1 unit
Trig csc, sec, cot
1/y (cosecant), 1/x (secant), x/y (cotangent)
pi/3 (60 degrees)
(1/2, √3/2)
For backwards non special angles
Figure out quadrant, inverse of trig is ref., calculate the ref angle chart
coterminal angles
add or subtract 360 degrees/2 pi
Reciprocal of tan
cot=A/O
30-60-90 triangle
x (side next to 60deg), x√3 (side next to 30deg), 2x (hypotenuse)
45-45-90 triangle
x, x, x√2
Trig sin, cos, tan
y (sine), x (cosine), y/x (tangent)
90 degrees=
π/2
Normal #
It's in radians
If the denominator is 2
It's in the axis
Don't plug _ in calc when going backwards
Negative
3 # fowards problem
Put in radiams
θ must be measured in
Radians (for arc length)
Quadrant 1 formula
Reference
Not the unit circle
SOH CAH TOA
SOH
Sin=Opposite/Hypotenuse
TOA
Tan=Opposite/Adjacent
S=
rθ
Arc length
s
θ=
s/r
Reciprocal of cos
sec= H/A
Reciprocal of sin
csc= H/O
radians to degrees
multiply by 180/pi
degrees to radians
multiply by pi/180
Quadrant 3 formula
pi/180+ref.
Quadrant 2 formula
pi/180- ref.
12 special angles of first quadrant
pi/6 (√3/2, 1/2), pi/4 (√2/2, √2/2), pi/3 (1/2, √3/2)
Backwards has_ answers unless on the _
2; axis
12 special angles of second quadrant
2pi/3 (-1/2, √3/2), 3pi/4 (-√2/2, √2/2), 5pi/6 (-√3/2, 1/2)
Quadrant 4 formula
2pi/360-ref.
12 special angles of fourth quadrant
5pi/3 (1/2, -√3/2), 7pi/4 (√2/2, -√2/2), 11pi/6 (√3/2, -1/2)
1 degree= (mins)
60 mins
1'=
60"
1°
60'
12 special angles of third quadrant
7pi/6 (-√3/2, -1/2), 5pi/4 (-√2/2, -√2/2), 4pi/3 (-1/2, -√3/2)
Decimal degrees and degrees mins seconds on calc
Control book then push triangle and type dd or dms
CAH
Cos=Adjacent/Hypotenuse
When can you use the degree button
For cowards not backwards calculations
