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PRECAL. TEST 2 REVIEW Name___________________________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 1) The equation θ2 = tan-1 (ωC/G) gives the phase angle of impedance in the parallel portion of a distributed constant circuit. Find θ2 if ω = 150 radians per second, C = 0.08 μF per kilometer, and G = 1.85 μsiemens per kilometer. Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. 2) sin x - sin x cosx = sin3 x 3) cos (x + π) = cos x Complete the identity. 4) (sin x + cos x)2 =? 1 + 2 sin x cos x Verify the identity. 5) cot θ ∙ sec θ = csc θ 6) csc2 u - cos u sec u= cot2 u 7) (1 + tan2 u)(1 - sin2 u) = 1 8) cot 2 x + csc 2 x = 2 csc 2 x - 1 Find the exact value of the expression. 9) cos (165°) cos (45°) + sin (165°) sin (45°) Use the given information to find the exact value of the expression. 4 2 10) sin α = , α lies in quadrant II, and cos β = , β lies in quadrant I 5 5 Find cos (α - β). Verify the identity. cos(α + β) 11) = cot β - tan α cos α sin β Use the given information to find the exact value of the expression. 7 2 12) sin α = , α lies in quadrant II, and cos β = , β lies in quadrant I 25 5 Verify the identity. π tan x - 1 13) tan x = 4 1 + tan x 1 Find cos (α - β). 14) cos 4θ = 2 cos2 (2θ) - 1 Solve the problem. 15) If a projectile is fired at an angle θ and initial velocity v, then the horizontal distance traveled by the projectile is 1 2 given by D = v sin θ cos θ. Express D as a function of 2θ. 16 Use a half-angle formula to find the exact value of the expression. 3π 16) sin 8 Use the given information to find the exact value of the trigonometric function. 6 θ 17) csc θ = - , tan θ > 0 Find cos . 5 2 Express the product as a sum or difference. 11x x 18) cos cos 2 2 Express the sum or difference as a product. 19) sin 75∘+ sin 15∘ Verify the identity. sin α - sin β α-β α+β 20) cot = tan sin α + sin β 2 2 Solve the equation on the interval [0, 2π). 3 21) cos 2x = 2 22) sin2 x - cos2 x = 0 23) tan x + sec x = 1 Solve the equation on the interval [0, 2π). 24) -tan2 x sin x = -tan2 x Find all solutions of the equation. 25) 2 cos x - 1 = 0 Solve the equation on the interval [0, 2π). 26) sin 2x + sin x = 0 Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 27) 2 sin2 x cos2 x 2 Find the exact value under the given conditions. 4 π 21 3π 28) cos α = - , , π<β< < α < π; sin β = 5 2 5 2 3 Find tan (α + β). Answer Key Testname: TST2412_REVIEW2 1) 80.2° π 2) 4 20) 3) 0 4) 1 cos cos θ 1 1 5) cot θ ∙ sec θ = ∙ = = csc θ sin θ cos θ sin θ 6) csc2 u - cos u sec u = csc2 u - cos u ∙ 7) (1 + tan2 u)(1 - sin2 u) = sec2 u ∙ cos2 u = α+β 2 α+β sin 2 1 = csc2 u cos u 1 = cot2 u sin α - sin β = sin α + sin β 1 ∙ cos2 u cos2 u =1 π 3π 5π 7π , , , 4 4 4 4 π 5π + 2nπ or x = + 2nπ 3 3 26) 0, 11) cos(α + β) cos α cos β - sin α sin β cos α cos β = = cos α sin β cos α sin β cos α sin β 27) sin α sin β cos β sin α = = cot β - tan α cos α sin β sin β cos α 1 1 - cos 4x 4 4 28) -6 + 4 21 8 + 3 21 π tan x - tan π/4 tan x - 1 . = = 4 1 + (tan x)(tan π/4) 1 + tan x 14) cos 4θ = cos[2(2θ)] = 2 cos2 (2θ) - 1 1 2 15) D = v sin 2θ 32 16) 1 2 19) 2 18 - 3 11 6 17) 18) 2+ 1 (cos 5x + cos 6x) 2 6 2 4 α-β α+β cot 2 2 22) -6 + 4 21 25 13) tan x - α+β α-β cos 2 2 π 11π 13π 23π , , , 12 12 12 12 25) x = -48 + 7 21 125 2 sin = tan 10) 12) α-β α+β cos 2 2 21) 23) 0 24) 0, π 8) cot 2 x + csc 2 x = csc 2 x - 1 + csc 2 x = 2 csc 2 x - 1. 1 9) 2 2 sin 2π 4π , π, 3 3 sin α-β 2 cos α-β 2 = ∙