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Regents Exam Questions A2.A.56: Determining Trigonometric Functions 2 Name: ________________________ www.jmap.org A2.A.56: Determining Trigonometric Functions 2: Know the exact and approximate values of the sine, cosine, and tangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles x 1 If f(x) = cos x + tan , then f(π) is 3 3 +3 3 1) 3 −3 3 3 +1 3 −1 2) 3) 4) 2 At x = 1) 2) 3) 4) π 5 If f(x) = sin2 x, then f equals 2 1) 1 3 2) 4 1 3) 2 1 4) 4 1 2 3 0 π 2 6 If f(x) = sinx + cos 2x, then f(π) is 1) 1 2) 2 3) 0 4) −1 , the difference 2sinx − cos 2x is 7 The value of sin π 3 The value of cos is 4 2 1) 2) 3) 4) 1 1 2 1 4 0 4 The value of sin 1) 2) 3) 4) 3 2 π 6 + tan π 4 is 1) − 2) 1 2 3) − 4) 0 3 +2 2 2 3+ 2 3 cos π is 3 2 1 2 8 What is the value of tan 1) 1+ π 2) 2 3) 4) 2 1 3 +3 3 3 −3 3 3 −1 3 +1 π 3 + cos π ? Regents Exam Questions A2.A.56: Determining Trigonometric Functions 2 Name: ________________________ www.jmap.org x 9 If f(x) = sin , find f(π) equals 4 1) 1 1 3 2) 2 1 3) 2 2 1 4) 2 10 The value of cos 1 2 1) 1 2) 1 2 3) − 4) −1 π 3 − sin 13 The numerical value of sin 1) 3π is 2 2) 2 2 3) −1 + 4) −1 2 2 2 2 π 14 If f(x) = sin2x + cos x, what is f ? 4 1) 1 2 1+ 3π π + cos is 2 4 2) 1 2 3) 4) π 11 If f(x) = cos 3x + sinx, then f equals 2 1) 1 2) 2 3) −1 4) 0 1+ 2 2 1+ 3 0 2 2 15 Find the value of sin2 16 Find the value of sin 3π − cos π is 12 The value of sin 3 2 1 1) −1 2 1 2) 1 2 1 3) 2 1 4) − 2 π 3 π 2 . − cos 3π . 2 17 If f x = 3cos x, find the numerical value of f π . π 18 If f(x) = 2cos x, find f . 3 19 What is the numerical value of the product tan π cos π ? 4 3 2 Regents Exam Questions A2.A.56: Determining Trigonometric Functions 2 Name: ________________________ www.jmap.org x 20 If f(x) = sinx + cos , find f(2π). 2 π 31 If f(x) = sin2x + cos x, find the value of f . 2 π 21 If f x = cos 2x, find f . 2 π 32 If f(x) = tanx, evaluate f . 4 22 If f(x) = cos x + sinx, find the value of f(x) when 3π . x= 2 23 If f(θ) = tan θ − 2cos θ , find f(π). 24 Evaluate: cos π 2 +sin 3π 2 x 25 If f(x) = 4sin , find f(π). 3 26 If f(x) = sin2 x + cos 2 x, find f( π 4 ). π 27 If f x = 2sin2 x + sinx + 1, find the value of f . 6 π 28 If f x = sin3x + cos x, what is f ? 2 1 29 If f x = sin x + 2cos x, evaluate f(π). 2 π 30 If f(x) = 2cos 2 x + sinx − 1, find the value of f . 2 3 ID: A A2.A.56: Determining Trigonometric Functions 2: Know the exact and approximate values of the sine, cosine, and tangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles Answer Section 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: 3 4 4 3 2 1 1 1 1 3 3 1 1 1 3 1 PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 PTS: 2 16 ANS: 1 REF: 018402siii PTS: 2 17 ANS: −3 REF: 068415siii PTS: 2 18 ANS: 1 REF: 018511siii PTS: 2 19 ANS: 1 2 REF: 088711siii PTS: 2 20 ANS: −1 REF: 068814siii PTS: 2 REF: 010408siii REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: REF: 068129siii 068437siii 088426siii 068528siii 089322siii 068924siii 088935siii 089025siii 019420siii 069531siii 069718siii 089722siii 010017siii 080317siii 1 ID: A 21 ANS: −1 PTS: 2 22 ANS: −1 REF: 019012siii PTS: 2 23 ANS: 2 REF: 069406siii PTS: 2 24 ANS: −1 REF: 089936siii PTS: 2 25 ANS: 2 3 REF: 019507siii PTS: 2 26 ANS: 1 REF: 069510siii PTS: 2 27 ANS: 2 REF: 019606siii PTS: 2 28 ANS: −1 REF: 019812siii PTS: 2 29 ANS: −1 REF: 019905siii PTS: 2 30 ANS: 0 REF: 069909siii PTS: 2 31 ANS: 0 REF: 010011siii PTS: 2 32 ANS: 1 REF: 060002siii PTS: 2 REF: 010102siii 2