HomeMath Class 11Trigonometry MCQ test 1 Trigonometry MCQ test 1 Trigonometry 11 CBSE - MCQ test 1 Question 1. Determine the quadrant that contains the terminal side of an angle measuring −7π/6. 1st Quadrent 2nd Quadrent 3rd Quadrent 4th Quadrent Click Here For Solution Solution: −7π/6 Convert into degree measure =−7π/6*180/π =-210° Terminal side of an angle measuring −7π/6 Will be in 2nd Quadrent, Question 2. Determine the quadrant that contains the terminal side of an angle x, such that tan x < 0 and sin x > 0. 1st Quadrent 2nd Quadrent 3rd Quadrent 4th Quadrent Click Here For Solution sin x > 0 ,tan x < 0 x is in 2nd Quadrent Question 3. Determine the quadrant that contains the terminal side of an angle x, such that cos x < 0 and sin x > 0. 1st Quadrent 2nd Quadrent 3rd Quadrent 4th Quadrent Click Here For Solution cos x < 0 and sin x > 0 x is in 2nd Quadrent Question 4. Determine the quadrant that contains the terminal side of an angle x, such that tan x > 0 and sin x > 0. 1st Quadrent 2nd Quadrent 3rd Quadrent 4th Quadrent Click Here For Solution tan x > 0 and sin x > 0 x is in 1st Quadrent Question 5. Determine the quadrant that contains the terminal side of an angle measuring −10π/3. 1st Quadrent 2nd Quadrent 3rd Quadrent 4th Quadrent Click Here For Solution −10π/3 Convert into degree measure =>−10π/3 *180/π =>-600° =>-600°/360° =>Remainder =-240° Terminal side of an angle measuring −10π/3 Will be in 2nd Quadrent, Question:6 If sin θ and cos θ are the roots of ax² – bx + c = 0, then the relation between a, b and c will be a2 – b2 + 2ac = 0 a2 + b2 + 2ac = 0 a2 – b2 - 2ac = 0 None Click Here For Solution sin θ and cos θ are the roots of ax² – bx + c = 0. Sum of roots= sin θ +cos θ = b/a Product of roots= sin θ.cos θ = c/a We know that, (sin θ +cos θ )²=sin²θ +cos²θ+2sin θ.cos θ=1+2sin θ.cos (b/a )²=1+2c/a (b²/a² )=1+2c/a b²=a² +2ca a2 – b2 + 2ac = 0 Question:7 If tan A = 1/2 and tan B = 1/3, then the value of A + B is : π/6 π/4 π/5 π/3 Click Here For Solution tan(A+B)=(tanA+tanB)/(1+tanA.tanB) tan(A+B)=(1/2+1/3)/(1-1/2*1/3) tan(A+B)=(5/6)/(5/6) tan(A+B)=(5/5)=tan45° (A+B)=45°=π/4 Question:8 The value of cos 1° cos 2° cos 3° … cos 179° is 1/2 1 object 0 None Click Here For Solution cos 1° cos 2° cos 3° ....... cos 179° => cos 1° cos 2° cos 3° ......... cos 90° cos 91° ......... cos 179° => cos 1° × cos 2° × cos 3° ..... × 0 × cos 91° .......... cos 179° (∵ cos 90° = 0) => 0 × finite => 0 Hence, cos 1° cos 2° cos 3° ......... cos 179° = 0 Question:9What would be the value of : sin 50° – sin 70° + sin 10° 1 0 -1 None of these Click Here For Solution Question:10 What would the value of (1 + tan α) (1 + tan β) , If α + β = π/4 1 -1 2 None Click Here For Solution Question:11 If A lies in the second quadrant and 3 tan A + 4 = 0, then the value of (2 cot A – 5 cos A + sin A) is equal to 48/7 10/23 23/10 None Click Here For Solution Question:12 Which of following is correct cos θ = x + (1/x), when ,If x is real. θ is an acute angle. θ is right angle. No value of θ is possible. None of these Click Here For Solution Question:13 If tanA + cot A = 2 and 0°< A < 90° then what is the value of tan^n A + cot^n A? 1 2 -1 None Click Here For Solution Question:14 If the value of α + β = 90°, and α : β = 2 : 1, then what is the ratio of cos α to cos β ? √3 √3:1 1:√3 1:3 Click Here For Solution Given,α : β = 2 : 1 Let α=2k,β=k Therefore , 2K+K=90° K=30° α=2k=60° β=30° cos60°=1/2 cos 30°=√3/2 cos α : cos β=1:√3 Question:15 If θ is said to be an acute angle, and 7 sin²θ + 3 cos²θ = 4, then what would be the value of tan θ? 1 √3 1/√3 None Click Here For Solution Question:16 If A is said to be an acute angle, and 4 cos² A - 1 = 0, then what is the value of tan (A - 15°)? 1 -1 √3 None of these Click Here For Solution Question:17 What would be be the value of 1 - 2sin² θ, if cos^4 θ - sin^4 θ = 2/3? Becomes zero 3/2 2/3 None Click Here For Solution (cos²θ)² - (sin²θ)² = 2/3 (cos²θ - sin²θ)(cos²θ + sin²θ) = 2/3 (cos²θ - sin²θ) = 2/3 (1-sin²θ - sin²θ) = 2/3 (1-2sin²θ ) = 2/3 Question:18 If sin (θ + 18°) = cos 60°, then Which of following is the value of cos5θ, where 0°< θ < 90°? 2:1 1:4 3:1 1:2 Click Here For Solution sin (θ + 18°) = cos 60° => cos (90° – 30°) = sin 30° => θ + 18° = 30° => θ = 30° – 18° = 12° ∴ cos5θ = cos 60° = 1/2 Question:19 If y = cosθ, then what is the maximum value of y? 2 0 -1 1 Click Here For Solution maximum value of cosθ=1 Therefore,maximum value of y=1 Question:20 If tan θ - cot θ = 0, what will be the value of sin θ + cos θ? 1 1/√2 2 √2 Click Here For Solution tan θ - cot θ = 0 tan θ =cot θ We know that, tan45° = cot45° = 1 so θ=45° sinθ+cosθ =>sin45°+cos45° =>1/√2+1/√2 =>2(1/√2) =>√2 Submit Newer Older
