28/03/2020 Trigonometry(Senior Class Maths Study by Topics) 0Comments by Gate Academy Welcome to your Trigonometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. 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 km5,005 km4,004 km6,006 km2. Given that tan²θ + sec²θ = 3, the value of θ (for 0°<θ<90°) is30 degrees45 degrees60 degrees90 degrees3. 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)121°24°76.4°14°4. The difference in longitude betweenP(55°N, 12°W) and Q(15°S, 65°W) is70°40°53°77°5. 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 distance between the two locations in km, is approximately(222θ) cos φ°(56φ) cosθ°(111φ) cosθ°(111θ) cos φ°6. If there is no stop-over at Dubai, and the average speed of the airplane is 500km/hr, the total time taken for the plane to fly from Lagos to Kuala Lumpur via Dubai is approximately8 h10 h7 h5 h7. Two places A and B are on the equator. The longitude of A and B are 25°W and 42°E, respectively. Find the distance between them along the equator.2454km7490km1220 km230km8. The angle of depression of a boat from the midpoint of a vertical cliff is 35°. If the boat is 120 m from the foot of the cliff, calculate the height of the cliff.1.74 m174 m16.8 m168 m9. 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 onlyI and III onlyII and IV onlyII and III only10. 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)6,006 km3,185 km4,004 km5,005 km11. Given that cot θ = m/n,cosec θ equalsn/m1/n (n²+m²)√(m/n)1/n √(n²+m²)12. cos 65° is equal tocos 295°cos 245°cos 115°sin 115°13. If cos θ > 0 and sin θ < 0, then180° < θ < 270°90° < θ < 180°270°< θ < 360°0° < θ < 90°14. A hunter on the ground observes a bird perching on a tree on a bearing of S15°W. The bearing of the hunter from the bird isN75°EN75°WN15°WN15°E15. Given that cos²θ - sin²θ = 1/8, find the value of tan θ3/√73√7√7√7/316. 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 is5, 005.0 km2,502.5 km2,359.4 km4,718.8 km17. If sin-¹(0.966) = 75°, then sin-¹(-0.966) equals75 or 105 degrees255 or 285 degrees195 or 285 degrees105 or 255 degrees18. 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 approximately111θ222θ167θ56θ19. The value of 2cos 270° + sin 270° is0-1-2120. A right-angled triangle has sides of lengths (3m-1) cm, (m) cm and (3m+1) cm. The value of m is26121821. A motorist travels from Abuja on a bearing of 150° to Kaduna 40 km away. From Kaduna he travels to Lagos on a bearing of 210°.If Lagos is located directly South of Abuja, how far is Lagos from Abuja?40√3 km40 km40√2 km80 km22. If tan θ = 5/12,then the value of sin θ - cos θ is12/137/13- 7/135/1323. If cosθ = x/y, then 1 + tan²θ equals(y² - x²)/ y²x²/y²(x² - y²)/ y²y²/x²24. 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 Georgia20 km40 km20√2 km30 km25. If sin θ = a/b, where θ is an acute angle,then cot θ equals√(b/ b²-a²)a/ √(b²-a²)√(b+a)(b-a)/ a√(b²-a²)/ b26 out of 25Time is Up! Time's up