Today is our topic of discussion Trigonometry exercises – 8.2 .
Trigonometry exercises – 8.2
Use calculator to solve the following problems. Use ( π=3.1416) as the approximate value of π in every case where necessary.
1. 1) Express in radians :
(i) 75°30′
(ii) 55°54′53″
(iii) 33°22’11”
2) Express in degrees:
(i) 8π/13 radian
(ii) 1.3177 radian
(iii) 0.9759 radian
2. If we express an angle by D° and R in radian and circular system then prove that, D/180 =R/π
3. The radius of a wheel is 2 metre 3 c.m. Find approximate value of its circumference to four places of decimals.
4. The diameter of the wheel of a car is 0.84 metre and the wheel makes 6 revolutions per second. Find the speed of the car.
5. The angle of a triangle are in the ratio 2 5 3; what are the circular measures of the smallest and the largest angles?
6. The angles of a triangle are in arithmetical progression and the largest angle is twice the smallest angle. What are the radian measures of the angles ?
7. The arc joining Dhaka with Chittagong subtends an angle of 5° at the centre of the earth. Taking the earth to be a sphere of radius of 6440 k.m. find the distance of Chittagong from Dhaka.
8. The arc joining Teknaf with Tetulia subtends an angle of 10°6′3″ at the centre of the earth. Taking the earth to be a sphere of radius 6440 k.m., find the distance of Tetulia and Teknaf.
9. Riding a bicycle Shahed traverses a segment of a circular path in 11 seconds. The diameter of the circular path is 201 metre and the angle subtended by the segment at the centre is 30°; find Shahed’s speed.
10. Given that the radius of the earth is 6440 k.m, what is the distance between the two places on the surface of the earth which subtend an angle of 32″ at the centre of the earth?
11. Express in radian the angle between the minute hand and hour hand of a clock when it is 9: 30 a.m. [Hint. One spacing on the dial subtends 360°/60=6° degree angle at the centre. At 9:30 A.M. (or P.M.) the hour and minute hands of the clock are (15+2×1/2) or 17 x1/2spacing a part]
12. A person jogging on a circular track at 6 k.m. per hour, traverses a segment of the path in 36 seconds which subtends angle of 60° at the centre. Find the diameter of the circular track.
13. A hill subtends an angle of 8′ at a point at a distance of 750 kilometre from the foot of the hill. Find the height of the hill.
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