Review 5.1 to 5.3

a) Add 3 sin2 x cos x + 2 sin2 x cos x. b) Expand (cos x – 1)2. cos2 x – 2cos x + 1 c) Multiply (2 sin x – 3)(3 sin x + 5). 6sin2 x + sin x - 15

Factor. a) 25 sin2 x - 4 (5 sin x + 2)(5 sin x – 2) b) 2tan2x – 2tanx – 40 2(tan x – 5)(tan x + 4) c) cos2 x sin3 x - cos2 x sin5 x cos2 x sin3 x (1 – sin2 x) = cos4x sin3 x d) 2 cos x – sin2 x - 7 (cos x + 4)(cos x – 2)

Simplify. a) cot x sec x csc x b) cos x + sec x (cos2x + 1)/cos x c) csc2 x – cot2 x cot2 x + 1 sin2 x d) 1 – tan2x 1 + tan2x cos2x – sin2x

Prove. a) 1 + 1 = 2 + 2 cot2 x 1 – cos x 1 + c0s x b) sec x + tan x = cos x 1–sin x

Solve. a) sin x = -.872 x ≈ 4.2 + 2πk or x ≈ 5.22 + 2πk b) 8tan x + 11 = 2 tan x + 5 x = 3π/4 + πk c) (sin x + 1)(4cos2x – 1) = 0 x = 3π/2 + 2πk or x = π/3 + πk or x = 2π/3 + πk d) 3cos x = 5 sin x x ≈ .54 + πk

and just a few more… a) 2sec x + 1= 5 x = π/3 + 2πk or 5π/3 + 2πk b) cos 2x = ½ x = π/6 + πk or 5π/6 + πk c) cos x + 2 sec x = -3 x = π + 2 π k d) sin x + 1 = cos x x = 2 π k or x = 3π/2 + 2 π k