Question

7. You are given that u is an angle in quadrant III with sin u -, and that w is an angle in the first quadrant with tan w = ? . Calculate the exact value of each one of the following: (You should show how you get your answer) (a) cos u (b) tanu (c) sin w (d) cos w (e) sin (u - w)

Answer 1

sinu -US= Perfendicular (P) Hypatinouse (H) calculate Base (B) using pythagorous theorem. (H)2 = (P)2+ (B)2 (5)2 = (W)+(B)2 (B) =-16 +25 B = 89 ) B=3 a) COSu - B su is negative -3 { As cosul quadrant en H (6) tanu 4 1 clos = tan w 18 Perpendicular (0) Base (B) Calculate hypotenouse isusing pythagorows theorem (14) = (P)2+(B)2 = (12)2+(5) =144 +25 H = √169 H=13 (c) Sin w= P. H 12 13 (d) Cosw= B H - 5 (e ) Sin(u-w) Sinu Cosw-cosu Sinw (*)(5) - (})( 1) Sin (u-w) = 16 65

- (f) Cos (w+4)= caso casu - sin wsinu 19) (-)-(3) + -4 5 Il -15 65 48 6S cos (wtu) - 33 65 3 3 3