28/03/2020 Trigonometry(Senior Class Maths Study by Topics) 28/03/2020 0Comments by Gate Academy Welcome to your Trigonometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. The value ofsin (870°) is -1/2 -0.866 1/2 0.866 2. If m and n are the lengths of the diagonals of a rhombus of side x, andm² + n² = kx², the value of k is 1 2 4 3 3. Two towns are θ° apart on the same meridian. If the earth's radius is 6,370 km π = 22/7, their distance apart in km is approximately 222θ 111θ 56θ 167θ 4. Three locations on the surface of the earth are Mumbai(45°N, 20ºE), Guanzhou(45°N, 40°E) and Ibadan(45°S, 40°E). Which of the following statements are correct?I. Guanzhou and Ibadan are on the same longitude.II. Guanzhou and Ibadan are on the same latitude.III. The difference between the longitudes of Mumbai and Guanzhou is 60°.IV. The difference between the latitudes of Mumbai and Ibadan is 90°. I and IV only I and III only II and IV only II and III only 5. If cos θ > 0 and sin θ < 0, then 180° < θ < 270° 0° < θ < 90° 270°< θ < 360° 90° < θ < 180° 6. The bearing of a point P from an observer Q is S37°W. The bearing of Q from P is S 53° W N 37° E S 37° E N 53° W 7. Three cities London, Seoul and Harare are such that Seoul is located 50 km away from London on a bearing of 065°. Harare is 100 km away from London on a bearing of 305°. The distance between Seoul and Harare is 50√7 km 50√5 km 50√3 km 50√2 km 8. Sin 38° has the same value as sin (-38°) sin 128° cos 308° sin 218° 9. The bearing of a point P from a point Q is 065°. What is the bearing of Q from P? 155° 245° 115° 295° 10. The values of θ for whichsin θ = cos θ are within the range 0° < θ < 360° 135° and 225° 45° and 135° 45° and 315° 45° and 225° 11. A girl walks 30 m from a point P on a bearing of 040º to a point Q. She then walks 30 m on a bearing of 140º to a point R. How far is R from P 38.6 km 30 km 42.4 km 25.2 km 12. If sin θ = a/b, where θ is an acute angle,then cot θ equals a/ √(b²-a²) √(b²-a²)/ b √(b/ b²-a²) √(b+a)(b-a)/ a 13. Toronto is on a bearing of 225°from Georgia. Texas is directly North of Toronto and directly West of Georgia. If Texas is located 20 km away from Georgia, how far is Toronto from Georgia 30 km 40 km 20√2 km 20 km 14. Simplify the expression can be simplified to 1-sinθ cosθ (1+cosθ)/ sinθ sinθ/(1-cosθ) 15. A young man 1.7 m tall, while standing, measures the angle of elevation of the top of a pole as 40°. If he is 15 m from the pole, what is the height of the pole? 9 m 12.5 m 20.2 m 14.3 m 16. A ladder of length 5m rests against a vertical wall and makes an angle 30° with the wall. How far is the foot of the ladder from the wall? 5/2 m 5 m 7.07 m 4.33 m 17. The angle of elevation of the top of a tree from a point P and the ground is 30°. From a point Q, 10 m closer to the foot of the tree, the angle of elevation is 45°.How tall is the tree? 10√3 m 5(√3 + 2) m 5(√3 + 1) m 10√2 m 18. Points X and Y are respectively 48m North and 20m East of point Z, The bearing of X and Y is approximately 067° 157° 247° 337° 19. If cosθ = x/y, then 1 + tan²θ equals x²/y² y²/x² (y² - x²)/ y² (x² - y²)/ y² 20. If sin θ = x, the value of tan θ for 0° < θ < 90° is x/x-1 x/√(x²-1) 1-x x/√(x²-1) 21. The value of sin(870°) is -1/2 -√3/2 √3/2 1/2 22. The diagonals of a rhombus are of lengths 10 cm and 24 cm.The length of each side of the rhombus is 13 cm 12 cm 17 cm 5 cm 23. An isosceles triangle of sides 65 mm, 65 mm and 50 mm is inscribed in a circle. The radius of the circle is 60 mm 35 mm 35.21 mm 40 mm 24. If the bearing of New York from Kansas city is 125°, the bearing of Kansas city from New York is? 55° 215° 305° 235° 25. Which of the following have the same value as sin 15°?I. sin 165°II. sin 285°III. sin (-15°)IV. sin (-195°) I and III only III and IV only I and IV only I and II only 1 out of 25 Time is Up! Time's up