Toomey
Harold’s Trigonometry“Cheat Sheet”7 February 2014Unit CircleTrig Chart(Quadrant I only)Degrees0°30°45°60°90°Radians0π/6π/4π/3π/2Sin (θ) 01/22/23/21Cos (θ) 13/22/21/20Tan (θ) = S/C03/313±∞Sin (θ) Pattern0212223242Graphical Representation Of The Trig Functions392272629387803 π003 π360984165100001133475169876001890699160020004154805179070004906314173355003397885165431003527291518920026438091404190048367952980690“All Students Take Calculus”00“All Students Take Calculus”5017770129857500The Six Trig “Levers”y = a sin (b (x - h)) + kGraphing TipsNotesMove up/down ?k (Vertical translation)k= (max + min)2If k = f(x) then x-axis is replaced by f(x)-axisMove left/right ?h (Phase shift)‘+‘ shifts rightsin (x)=cos (x-π/2)Stretch up/down ?a (Amplitude)a= (max – min)2a is NOT peak-to-peak on y-axisStretch left/right ?b (Frequency ? 2π)T=2πb= 1?T = peak-to-peak on θ-axisT = π/b for tan (bx)Flip about x-axis a → –af(x) → –f(x)Odd Function: sin (x)=-sin (-x)Flip about y-axisb → –bf(x) → f(-x)Even Function: cos (x)=cos (-x)Harold’s Trigonometry“Cheat Sheet”7 February 201445-45-90 Triangle30-60-90 TriangleProof:a? + b? = c?x = yx? + x? = 1?2x? = 1x? = ?x2= 12x= ± 12= ±12= ±22= 22Proof:a? + b? = c?y? + (?)? = 1?y? + ? = 1y? = ?y2= 34y= ± 34= ±34= ±32= 32Radians and Arc LengthRadian = arc length (s) of a unit circles = r θC = π D = π (2r) = 2π rProof:If r = 1 (unit circle)then s = (1)θ = θ and C = 2π 1=2πTherefore 360° = 2π radiansTo convert degrees to radians:n° x π rad180° = m radians ................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.