Mastering Trigonometry for Quantitative Aptitude (Chapter-12): 100 MCQS to Ace Competitive Exams in India December 31, 2023 Quantitative AptitudeTest 1Test 2Test 3Test 4Test 5 Report a question What's wrong with this question?You cannot submit an empty report. Please add some details. 0% Trigonometry Practice Questions Test-320 MCQs20 Marks10 Minutes 1 / 20If sin(x + 54°) = cos x, where 0 < x, x + 54° < 90°, then what is the value of x? 54° 18° 36° 27° EXPLANATION:Given, sin (x + 54°) = cos x ⇒ sin (x + 54°) = sin (90° - x) (∵ 0° < x < 90°) ⇒ x + 54° = 90° - x ⇒ 2x = 36° ⇒ x = 18° 2 / 20The value of the expression [cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)] is −1 1 1/2 0 EXPLANATION:Since cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ) = cosec (75° + θ) – cosec [90° – (15° – θ)] – tan (55° + θ) + tan [90° – (35° – θ)] = cosec (75° + θ) – cosec (75° + θ) – tan (55° + θ) + tan (55° + θ) = 0 3 / 20A wheel makes 12 revolutions per min. The angle in radian described by a spoke of the wheel in 1 s is 4π/5 5π/2 2π/5 3π/5 EXPLANATION:In 1 min = 60s, distance travelled by the wheel = 12 × Its circumference = 12 × 2 π r ∴ In 1 s distance travelled by the wheel = (12×2πr)/60 = 2πr/5 ∵ Angle = Ram/Radius = (2πr/5)/r Which is the required angle. 4 / 20If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is 4 : (√5 – 1) (√5 – 1) : 4 none of these 5 : 4 EXPLANATION:Given, the angles of a triangle be in the ratio 1 : 4 : 5 ⇒ x + 4x + 5x = 180 ⇒ 10x = 180 ⇒ x = 180/10 ⇒ x = 18 So, the angle are: 18, 72, 90 Since a : b : c = sin A : sin B : sin C ⇒ a : b : c = sin 18 : sin 72 : sin 90 ⇒ a : b : c = (√5 – 1)/4 : {√(10 + 2√5)}/4 : 1 ⇒ a : b : c = (√5 – 1) : {√(10 + 2√5)} : 4 Now, c /a = 4/(√5 – 1) ⇒ c : a = 4 : (√5 – 1) 5 / 20Consider the following statements for 0 ≤ q ≤ 90°. I-The value of sin θ + cos θ is always greater than 1. II-The value of tan θ + cot θ is always greater than 1. Which of the above statements is/are correct? Only II Both I and II Only I Neither I nor II 6 / 20If tan 8θ = cot 2θ, where 0 < 8θ < , π/2 then what is the value of tan 5θ? √3 1 1/√3 0 7 / 20The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles. If the side b is 2, then the angle B is 60° 90° 120° 30° EXPLANATION:Let the lengths of the sides if ∆ABC be a, b and c Perimeter of the triangle = 2s = a + b + c = 6(sinA + sinB + sinC)/3 ⇒ (sinA + sinB + sinC) = ( a + b + c)/2 ⇒ (sinA + sinB + sinC)/( a + b + c) = 1/2 From sin formula,Using sinA/a = sinB/b = sinC/c = (sinA + sinB + sinC)/(a + b + c) = 1/2 Now, sinB/b = 1/2 Given b = 2 So, sinB/2 = 1/2 ⇒ sinB = 1 ⇒ B = π/2 8 / 20What is (cosec x – sin x) (sec x – cos x) (tan x + cot x) equal to ? sin x – cos x sin x + cos x 2 1 9 / 20If 0 < x < π/2 , then (sin x + cosec x) is ≤ 2 > 2 < 2 ≥ 2 EXPLANATION:Since we are given that 0 < x < π/2, then sin 0 < x < sin π/2 ⇒ 0 < sin x < 1 ....(1) Similarly, cosec 0 > cosec x > cosec π/2 ⇒ ∞ > cosec x > 1 ....(2) Adding (1) and (2), we get ∞ > sin x + cosec x > 2 Thus, we can say that the value of the sum of the two trigonometric functions would be ≥ 2. 10 / 20If A, B, C and D are the successive angles of a cyclic quadrilateral, then what is cos A + cos B + cos C + cos D are equal to? 4 2 0 1 11 / 20If 1 + tan θ = √2 , then what is the value of cot θ – 1? 1/2 √2 1/√2 2 12 / 20If cos a + 2cos b + cos c = 2 then a, b, c are in b² = a × c 2b = a + c a = b = c None of these 13 / 20If cos ≥ 1/2 in the first quadrant, then which one of the following is correct? θ ≤ π/3 θ ≤ π/6 θ ≥ π/3 θ ≥ π/6 EXPLANATION:We know that, if value of cos θ increases, then the value of θ decreases. ∵ cos θ ≥ 1/2 ∴ cos θ ≥ cos π/3 θ ≤ π/3 14 / 20If x and y are complementary angles, then sec x = cosec y tan x = tan y cos x = cos y sin x = sin y 15 / 20The Earth takes 24 h to rotate about its own axis. Through what angle will it turn in 4 h and 12 min? 70° 64° 63° 65° EXPLANATION:∵ In 24 h, the Earth rotate about its own axis = 360° In 1 h the Earth rotate about its own axis = 360°/24 = 15° In 4 h the Earth rotate about its own axis = 15° × 4 = 60° Since, in 60 min the Earth rotate about its own axis = 15° In 12 min the Earth rotate about its own axis = 15°×12/60 = 3° ∴ In 4 h 12 min the Earth rotate about its own axis = 60° + 3° = 63° 16 / 20If x + y = 90°, then what is √(cos x cosec y - cos x sin y) equal to? √sin x cos x sin x √cos x 17 / 20From the top of a hill, the angles of depression of two consecutive km stones due east are found to be 30º and 45º. The height of the hill is 1/2(√3 +1) km (√3-1) km 1/2(√3 1) km (√3+1) km 18 / 20If ΔABC is right angled at C, then what is cos (A + B) + sin (A + B) equal to? 1 0 1/2 2 19 / 20The shadow of a vertical tower on level ground increases by 10 m when the altitude of the sun changes from 45º to 30º . The height of the tower is 5 (√3 +1) m 10 (√3+1) m 13 m 9 m 20 / 20A unit radian is approximately equal to 57° 17' 49'' 57° 16' 22'' 57° 17' 43'' 57° 17' 47'' Previous 1 2 3 4 5 6NextRelated Posts Profit and Loss MCQs (Chapter-4): 100 Essential Questions for Competitive Exams in India Percentage Mock Test (Chapter-3): 100 Important MCQs for Every Competitive Exam Average- Mean, Median & Mode (Chapter-1): 110 Important MCQs for Indian Competitive Exam PrepLeave a Reply Cancel Reply Save my name, email, and website in this browser for the next time I comment. I have read and accepted the Privacy Policy * Δ