Trigonometry

mpx

drawing

Solve these equations for .

Give your answers as a multiple of

.
(a)

(b)

2. A circle has radius 4 cm . The perimeter of a sector of the circle is equal to the area of the sector. Find the angle in the sector, giving your answer in degrees to 1 decimal place.
3. (a) When

is small, show that

can be approximated by

.
(b) Hence, approximate the value of

.

Calculate the percentage error in your approximation to 3 significant figures.
4. The diagram below shows the cross section of a cylinder of radius 2.5 m . A belt is wrapped around the cylinder and passes through a point 5 metres from the centre of the cylinder.

Find the length of the belt.
5. (a) Sketch the graph of

for

,
(b) Sketch the line

on the same axes, and indicate the point where the graphs intersect.

Use small angle approximations to find an approximate value for the

-coordinate of the intersection point.
6. Find the perimeter and area of the shaded sections of these shapes.
(a)

(b)

drawing