Question

Analytic Trig

Use Unit Circle

1. Find the exact value of .... under give conditions (please see photo below)

Find the exact value of cos (a + b) under the given conditions: tana 4. 4<a<n; cosß 2, 0<B<1 3 2

Answer 1

Solchon since 1/₂<a ca We know that sece = I Vi+3) seca = ± √ 1 + 1 secx = 1 a Again Given that cosB = / OLBLA/ Given tank = -/- /<<<2 qis second quadrat sine is positive and cost is negative in second quadrant know that seca-kanaal a seca= & ſtrana = 1 513 (54 - + 3 [ ' secka Cos] siace 1/2 <act, then cosa =-315 and also sinta + cosa al sina aſ1 - cosa & sine = - 1-(-3/4" = sine = V 25-5 - Ives - 7465 since / CLLA sinx=415 since o<BLE/ B is Arst quadrant tot know all trig function are positive in first quadrant know that sing+cosis a smB - I Vi-cos's -IVI-cme == V1-V4 = VE == sin B a 25 then علما B12 Since oLPLEI,

Hr Here 1/2 cose= -315 Sinka (OSB = sinB = 4/5 83/2 NOW cos (x+P) = Cosa COSBE sina sinß = 10 = (3/3)*(12) - (45)x("%) // 413 + 483 37 lo Hence cos (a+P) = (3 +413) = 10