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. If cos θ > 0 and sin θ < 0, then 270°< θ < 360° 0° < θ < 90° 90° < θ < 180° 180° < θ < 270° None 2. An observer on the ground views an airplane of altitude 1,000 m at an angle of elevation of 30°. How far is the plane from the observer? 1,000 m 500 m 2,000 m 1154.7 m None 3. Two towns P(θ°N, 7°E) and Q(θ°N, 29°W) are separated by a distance of 2,002 km, measured along the parallel of latitude. If R = 6,370 km and π = 22/7, the value of θ is 60° 30° 90° 45° None 4. Two cities London and Lagos are on latitude 60°N and their longitudes are 17°W and 28°E respectively. If R = 6,370 km and π = 22/7, the distance between London and Lagos, measured along the parallel of latitude is 2,502.5 km 4,718.8 km 5, 005.0 km 2,359.4 km None 5. An isosceles triangle of sides 65 mm, 65 mm and 50 mm is inscribed in a circle. The radius of the circle is 35.21 mm 40 mm 35 mm 60 mm None 6. Two locations on the equator are on longitudes 20°W and 70°E respectively. If R = 6,370 km and π = 22/7, their distance apart along the equator, correct to 2 significant figures is 10,000 km 11,000 km 15,000 km 5,600 km None 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√2 km 50√5 km 50√3 km 50√7 km None 8. 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°. II and IV only I and III only II and III only I and IV only None 9. If sinθ = 1/2 and 0° < θ < π/2, evaluate √3/4 4√3 √3/2 4/√3 None 10. If the shadow of a pole 7 m high is half of its length, what is the angle of elevation of the sun 12° 34° 23° 63° None 11. Two locations on the parallel of latitude φ°S have a difference in longitude of θ°. If R = 6,370 km and π=22/7, the circumference of the parallel of latitude in km, is 20,020 cos θ° 40,040 cos φ° 6,370 cos θ° 6,370 cos φ° None 12. The angle between latitudes 47°S and 21°N is 34° 68° 78° 26° None 13. If the radius of the earh is 6,370 km, the distance between two towns on latitudes 25°N and 20°S on the same meridian is (π = 22/7) 3,185 km 4,004 km 5,005 km 6,006 km None 14. The values of θ for whichsin θ = cos θ are within the range 0° < θ < 360° 45° and 135° 45° and 315° 45° and 225° 135° and 225° None 15. The values of tan 225° and tan 315° are respectively 1 and 1 1 and -1 -1 and -1 -1 and 1 None 16. The diagonals of a rhombus are of lengths 10 cm and 24 cm.The length of each side of the rhombus is 13 cm 5 cm 17 cm 12 cm None 17. The angle of elevation of the top of a tower from an observer on the ground is 60°. If the top of the tower is 100 m away from the observer, how high is the tower? 200 m 86.6 m 173.2 m 50 m None 18. A triangle has sides of lengths y cm, (y-4) cm and (y+4) cm. If the largest angle of the triangle is cos-1 (1/5), find the value of y 90/7 cm 20 cm 28 cm 24 cm None 19. If cos θ = -½, the values of θ could be -60 or 120 degrees 120 or 300 degrees -60 or 240 degrees 120 or 240 degrees None 20. The value of is -2 1 0 2 None 21. Cotonou and Niamey are on the same line of longitude and Niamey is 7°N of Cotonou. If the radius of the earth is 6400 km, how far is Niamey North of Cotonou along the line of longitude in km, π = 22/7 123km 540km 643km 782km None 22. The pilot of an airplane flying at an altitude of 2 km observes a landmark at an angle of depression of 25°. A few seconds later, he observes the landmark at an angle of depression of 50°. The distance between the two points of observation in km is 2(cos 25° - cos 50°) 2(cot 25° - cot 50°) 2(tan 50° - tan 25°) 2(sin 50° - sin 25°) None 23. P and Q are two places on the equator. The shortest distance between them along the equator is 8500 km. Find the angle between P and Q. (Take R =6,370 km, π= 3.142) 14° 121° 24° 76.4° None 24. Without using tables, evaluate sin(- 1320°) -0.866 -1/2 1/2 0.866 None 25. For any value of θ, the value ofis cos²θ sin²θ 1 2 None 1 out of 25 Time's upTime is Up!