Welcome to your Trigonometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. If m and n are the lengths of the diagonals of a rhombus of side x, andm² + n² = kx², the value of k is 4 3 2 1 2. The value of is 2 -2 1 0 3. If cos θ = -½, the values of θ could be -60 or 120 degrees 120 or 240 degrees 120 or 300 degrees -60 or 240 degrees 4. Points X and Y are respectively 48m North and 20m East of point Z. The distance /XY/ is 44m 52m 68m 60m 5. 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(tan 50° - tan 25°) 2(sin 50° - sin 25°) 2(cot 25° - cot 50°) 6. 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. 2454km 7490km 230km 1220 km 7. If sinθ = 1/2 and 0° < θ < π/2, evaluate 4√3 √3/2 √3/4 4/√3 8. 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 9. If cos θ = 4/5, then for 0° < θ < 90°, tanθ is equal to 4/3 5/3 3/4 5/4 10. The bearing of N75°W can also be expressed as 165° 075° 225° 285° 11. 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 cos 38° 40 cot 38° 40 sin 38° 40 tan 38° 12. Simplify the expression can be simplified to (1+cosθ)/ sinθ cosθ 1-sinθ sinθ/(1-cosθ) 13. 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 Y and Z along the meridian is 2,502 1/2 km 3,336 2/3 km 1,668 1/3 km 5,005 km 14. 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° (111φ) cosθ° (111θ) cos φ° (56φ) cosθ° 15. 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 25.2 km 30 km 38.6 km 42.4 km 16. The latitudes on which the radius of the parallel of latitude is one-half of the earth's radius are 30°N and 30°S 60°N and 60°S 30°N and 60°S 60°N and 30°S 17. 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 60 mm 35 mm 40 mm 18. If tan θ = 5/12,then the value of sin θ - cos θ is 5/13 12/13 7/13 - 7/13 19. If cos θ > 0 and sin θ < 0, then 180° < θ < 270° 90° < θ < 180° 0° < θ < 90° 270°< θ < 360° 20. Sin 38° has the same value as sin (-38°) sin 128° cos 308° sin 218° 21. X and Y are two lakes on the earth's surface. X has a latitude 34°N and Y has latitude 15°S. If the lakes are on the same meridian ,calculate the distance between them along the meridian(Take 2πR = 40,000 km) 540km 23km 54km 5440km 22. The angle between latitudes 20°N and 74°N is 54° 62° 74° 94° 23. Point P(60°S,22°E) lies on the same latitude as point Q. If the distance PQ measured along the parallel of latitude is 5,oo5 km, the radius of the earth is 6.370 km and π = 22/7, the longitude of point Q is 30°W 67°E 68°W 30°E 24. 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 II only III and IV only I and III only I and IV only 25. If tan θ = 2/3, then sec²θ equals 4/13 13/9 13/4 9/13 1 out of 25 Time is Up! Time's up