Trig Quick Notes
Conversions
Rad to Deg = *(180/pi)
Deg to Rad = *(pi/180)
Arc Length
s = r(theta)
For Angle: s / r = theta
Theta in Rad
Angular Speed
Stoichiometry to desired units
2 pi rad / 1 Rev
Find Ratios
SOH CAH TOA
Csc H/O, Sec H/A, Cot A/O
Pythagorean for unknowns
Identities
Review Identity Sheet
Graphing
Amp = Coe cient (A), y-axis
Stetch = Whole #, Shrink = Frac
Period = 2pi/b
Increments = 1/4 * Period
Phase Shift = -c/b
Sin = Hills, Up First
Cos: Valley, down rst
Tan: Ski Slope, up last
Sec = cos inverted piecewise
Csc = sin inverted piecewise
Cot = x re ected tan
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Observer Problems
Set up tan x = (h/l+y) and simplify
Set h = h and solve for L
Use nal position for L
Plug in L into original equation
Find Exact Value
Half Angle: Multiply x/2 for theta/apa.
Simplify, square unit circle values
Double Angle: Get cos/tan a/b using Pythagorean, unit circle or STs:
30-60-90: L, L sqrt(3), 2L
45-45-90: L, L, L sqrt(2)
Simplify and radicalize denominator it needed
Veri
1.
2.
3.
cations
Find common denominator
Look for places to create identities from combining or separating terms
Check with result
Evaluations
Use half or double angle identities, then Pythagorean theorem to determine
values and simplify
Unit Circle Exact Values
Sqrt(3) / 2 = 0.866
Sqrt(2) / 2 = 0.707
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-360 for all values 361+ to determine resultant solution