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 values of tan 225° and tan 315° are respectively -1 and 1 1 and 1 1 and -1 -1 and -1 2. If cos θ = 4/5, then for 0° < θ < 90°, tanθ is equal to 5/3 5/4 4/3 3/4 3. The value of sin(870°) is 1/2 √3/2 -√3/2 -1/2 4. cos 65° is equal to cos 245° cos 295° sin 115° cos 115° 5. A tree on the bank of a river is 24 m tall. If the angle of depression of a point on the opposite bank of the river is 30°, the width of the river is 41.569 m 12 m 24 m 13.856 m 6. 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) 6,006 km 3,185 km 4,004 km 5,005 km 7. An observer standing on the top of a building 40 m high views a stone on the ground level at an angle of depression of 38°. The distance of the stone from the foot of the building in metres, is equal to 40 cot 38° 40 tan 38° 40 cos 38° 40 sin 38° 8. 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 4,718.8 km 2,359.4 km 5, 005.0 km 2,502.5 km 9. If the radius of the earth is 6,370 km, the distance between two towns on latitudes 25°N and 20°S on the same meridian is (π = 22/7) 5,005 km 6,006 km 4,004 km 3,185 km 10. The sine, cosine and tangent of 240° are, respectively √3/2, -1/2 and √3 √3/2, 1/2 and √3 -√3/2, -1/2 and √3 -√3/2, 1/2 and -√3 11. sin 38° has the same value as sin 218 sin (-38) sin 128 cos 308 12. Starting from town X(45°N, 17°E), an airplane flies to town Y(45°N, 47°E) along the parallel of latitude and later to a third town Z(60°N, 47°E) along the meridian.(R = 6,370 km, π= 22/7). The distance between X and Y along the parallel of latitude in km, is 5,005√3/ 2 5,005√2/ 3 5,005 5,005√2/ 3 13. 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 56θ 222θ 167θ 111θ 14. Without using tables, evaluate sin(- 1320°) 0.866 -1/2 1/2 -0.866 15. A bearing of 310°, expressed as a compass bearing is N 40° W S 40° W S 50° W N 50°W 16. 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(sin 50° - sin 25°) 2(tan 50° - tan 25°) 2(cos 25° - cos 50°) 2(cot 25° - cot 50°) 17. The hypotenuse of a right-angled isosceles triangle is 8 units. The length of each of the other sides are 4(√2-1) 4 4/√2 4√2 18. If the bearing of New York from Kansas city is 125°, the bearing of Kansas city from New York is? 235° 55° 305° 215° 19. In a triangle PQR, <PQR = 60°, PQ = 3 cm and QR = 4 cm. Find |PR| 5 cm 2√5 cm √13 cm 2√3 cm 20. Simplify the expression can be simplified to cosθ sinθ/(1-cosθ) (1+cosθ)/ sinθ 1-sinθ 21. 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? 50 m 86.6 m 173.2 m 200 m 22. The value ofsin (870°) is -0.866 0.866 1/2 -1/2 23. The diagonals of a rhombus are of lengths 10 cm and 24 cm.The length of each side of the rhombus is 12 cm 17 cm 13 cm 5 cm 24. If sin-¹(0.966) = 75°, then sin-¹(-0.966) equals 255 or 285 degrees 105 or 255 degrees 75 or 105 degrees 195 or 285 degrees 25. Given that tan²θ + sec²θ = 3, the value of θ (for 0°<θ<90°) is 90 degrees 60 degrees 45 degrees 30 degrees 1 out of 25 Time is Up! Time's up