My Pack of Trigonometry Fun
C2 Chapter 10 1Special angles
1. i.Show that each of the following can be expressed in the form , where a is
an integer.
a. b. c. d. e.
(5)
2. The diagram shows a right-angled triangle ABC where and
i.Write down an expression for and show that .(2)
ii.Hence show that for all angles. You should give separate consideration to any special cases. (3)
iii.Use the triangle to show for all angles .
Explain why this relationship is not valid in the cases when and
(5)
3. Find the value of each of the following. You must show your working.
i.ii.
iii.iv.
v.vi. (18)
4. i. Given that , find the exact value of a.(2)
ii.Verify that (3)
iii.Find the value of (2)
C2 Chapter 10 2 Solution of trigonometric equations
1. Solve each of the following equations for
i.ii.
iii.iv.
v.vi.
(12)
2. Solve each of the following equations for . Give all answers correct
to one decimal place.
i.ii.
iii.iv.
(8)
3. It is given that where .
i.Use the fact that to show that .
(4)
ii.Use an appropriate identity to find the value of.
(2)
4. Solve each of the following equations for
i.ii. iii.
(12)
5. Solve the equation for
(4)
6. For each of the following equations, use an appropriate identity to find their solution
. Give answers correct to one decimal place where appropriate.
i.(6)
ii.(6)
iii.(3)
iv.(5)
v. (8)
C2 Chapter 10 3Triangles without right angles
1. For each of the following triangles (not drawn to scale), use the sine rule to find the
length of the side labelled x. Give each answer correct to 1 decimal place.
i.
(3)
ii.
2. i. Given that , write down the exact value of .(1)
The diagram shows triangle ABC, together with a line pointing due North. Point C
lies due East of A.
ii.Show that the area of triangle ABC is cm2(2)
iii.Use the cosine rule to
a. show that the length of AB = 19 cm,(3)
b. find angle, correct to the nearest whole degree.(3)
iv.Find the bearing of;
a. B from C(2)
b. A from B (to the nearest whole degree).(2)
C2 Chapter 10 4Circular measure
1. Convert each of the following angles into degrees. Give answers correct to one
decimal place where appropriate.
i.ii. iii. iv. (4)
2. Convert each of the following angles into radians. Express each answer in terms of
i.ii. iii. iv. (4)
3. The diagram shows the sector of a circle with radius 8 cm and centre C. Points A and
B lie on the circle and subtend an angle of radians at the centre.
i.Show that the length of the minor arc AB shown in the diagram is cm. (1)
ii.Find the perimeter of the sector. Give your answer correct to 1 decimal place. (2)
iii.Calculate the size of angle giving your answer in terms of . (2)
4. In the diagram, A and B are points on the circumference of a circle which has centre C
and radius 9 cm. Angle radians and sector ACB has area 56.7 cm2.
i.Show that and hence show that triangle ACB occupies approximately 70% of sector ACB. (4)
ii.Calculate the length of the chord AB, correct to 1 decimal place. (3)
C2 Chapter 10 5More trigonometrical graphs
1. The diagram shows the graph of for
i.On the same pair of axes, sketch the graph of for .(2)
ii.Hence, or otherwise, solve the equation
a. for (2)
b. for (2)
2. i.Describe the transformation which maps the graph of onto the graph of . (2)
ii.On the same pair of axes, sketch the graph of and for , labelling each graph clearly. (2)
iii.Verify that the graphs and intersect at the point . Hence, with reference to your sketch, write down the solution to the inequality for .
(3)
3. i.Use the identity to solve the equation for
(5)
ii.On the same pair of axes, sketch for , the graphs of and. Clearly label the points where the two graphs intersect with their
co-ordinates.
(3)
4. i.Sketch the graph of for
(2)
ii.With reference to your sketch, state the values of k for which the solution to the equation for consists of exactly two values of x.
(2)
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