Trigonometry summary, Lecture notes of Trigonometry

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_ Trigonometry 4, Angles between 0” and 90" sin © = opposite. cos = adjacent tan 0 * opposite y 4 hypstenuse- hypotenuse. adjacent A oJ snf = Y eso = fond = x r r % singo” =} singo* = sins" = a €0530° cosa” 2 cos" A fan30° =F tan 60" = VF tand5* 1 4 * the unit circle ' enter: 0 (origin) + radius + 4 unit * for ony acute angle between OP and x-axis: Plry) “ 1 na aka. basic angle / reference angle Ke fo sinO = 0 of eosO = A & z ple le bs Mi a. Angles + calculated anti-clockwise fiom the x-oxis = te value. aN . * 4” ord it . (#)150' a quadrant == SS 3rd a . quadrant] — quadkunt 4 “~ NW” suse a CAST diagram to decide whether sin, eS or ton is tve or -ve Ton Cos te only. sve only, % (odjacent) 3. Tigonometvie. graphs amptude » 4 + period: 360° (repeats every 360°) * rotational order of 2 about the origin. (in a 360°, it looks the some 2 times) 416 sn 8 64 einirum maximum \ ive + period: 360° - - ~ symmetrical about y-axis ve fn LAS nO SA 4. Tnverse trig functions "ye sine posing ‘domain: domain: OF 528 ranges 1 eos #1 domon: Zayed vange:tans an “ye sin “ye tone ye cos YP forte domain: range: domain racge: 0 = e0s 5. Trigonometric. equations Ex: solve sinu = 0.5 for - 360% x¢ 360° “use caleulator tp find «= 20" b& use symmetry of graph to find remaining values > 4 values total » Rule 4. snf = ¥ (2) y 4 r tond= fo + AT! — | tanB= snd eos x (2) os A 4 r r * for al 8, wih cos 8 #0 = is an idertity. _ = true for ALL values of x toanx |=) sinx cose — | cos*8 + sn B= 4 | for all 8. six + osx = 4