28/03/2020Trigonometry(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. 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 √32. From a point P 30 m away from the foot of a tree, the angle of elevation of the top of the tree is 30°. From a point Q on the opposite side of the tree, the angle of elevation of the top of the three is 45°. The distance between P and Q is50 m47.3 m42 m17.3 m3. 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 IV onlyI and II onlyIII and IV onlyI and III only4. If tan θ = 5/12,then the value of sin θ - cos θ is5/137/13- 7/1312/135. In a triangle PQR, <PQR = 60°, PQ = 3 cm and QR = 4 cm. Find |PR|2√5 cm√13 cm2√3 cm5 cm6. The hypotenuse of a right-angled isosceles triangle is 8 units. The length of each of the other sides are4√24(√2-1)44/√27. From an observation point close to the edge of the sea, a ship is 14 km away on a bearing of 130°.A second ship is 48 km away on a bearing of 220º. The distance separating the ships is34 km55 km50 km62 km8. 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)76.4°121°24°14°9. An inelastic string of length 1.0 m anchored to a point X has a stone tied to the end Y.How high does the stone rise when the string XY is inclined at 30° to the original vertical position?1/2 m1.155 m0.134 m0.866 m10. 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 is15,000 km10,000 km5,600 km11,000 km11. For any value of θ, the value ofis2cos²θsin²θ112. A woman 1.65 m tall stood 50 m away from the foot of a tower and observed that the angle of elevation pf the top of the tower to be 50°. What is the height of the tower?23m12 m24.5 m61.2 m13. Given that sin θ = √3/2 and cos θ = -½. The value of θ is240 degrees150 degrees120 degrees300 degrees14. Without using tables, evaluate sin(- 1320°)-1/20.8661/2-0.86615. 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 approximately10 h7 h5 h8 h16. Two cities are both on longitude 55°E. If their latitudes are 5°S and 65°S and R = 6,400 km, their distance apart in km is3,200π / 322,400π / 96,400π6,400π / 317. If cos θ > 0 and sin θ < 0, then90° < θ < 180°270°< θ < 360°0° < θ < 90°180° < θ < 270°18. Simplify the expression can be simplified to(1+cosθ)/ sinθsinθ/(1-cosθ)1-sinθcosθ19. The value of 2cos 270° + sin 270° is10-1-220. 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 km80 km40√2 km21. 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 to40 cot 38°40 tan 38°40 sin 38°40 cos 38°22. 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 km4,004 km5,005 km3,185 km23. 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 is5,005 km3,336 2/3 km2,502 1/2 km1,668 1/3 km24. Sin 38° has the same value assin 128°cos 308°sin (-38°)sin 218°25. 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(56φ) cosθ°(111θ) cos φ°(222θ) cos φ°(111φ) cosθ°26 out of 25Time is Up!