Examination of Trigonometry for grade X

Solve these following questions

1. Calculate the length of arc, whose locus is described by a radius R and angle X,
where :
a. R = 2 m and X = 1 radian
b. R = 3.67 km and X = 6.28 radians

2. The sector OAB, of a circle has radius R and perimeter 10 cm. The arc AB subtends
an angle X at the centre. If the area of the sector is A cm^2, show that :
a. A = 5R - R^2
b. the maximum area is 6.25, and what value of X does it occur?

3. A fisherman casts a distance of 80 m, during which the reel spins for 1.8
seconds. Calculate the rate of rotation in radians per second of the reel, which
has a 4 cm diameter. What assumptions have been applied in the answer?

4. Prove that: 1 + tan X. sin X. sec X = tan X. cosec X. sec X

Submit all of your work by mail, before Monday, 29th November, 2010