1. Trigonometry Revision Booklet Introduction to Trigonometry
Name:________________________________
Introduction to Trigonometry
Definition: Trigonometry is the study of triangles and their angles, their area and the lengths of their sides.
Important: You will need to make sure you calculator is in Degrees (DEG Mode) in order to complete questions on trigonometry and you must also be familiar with the following pages in the log tables
Pages:

2. a2 +b2 = c2 PYTHAGORAS THEOREM
The square of the hypotenuse is equal to the sum of the squares on the other 2 sides.
Remember: This theorem only works for Right Angled Triangles).

4. RIGHT ANGLED TRIANGLES
HYPOTHENUSE
HYPOTHENUSE
OPPOSITE
ADJACENT
900 A
900
ADJACENT
OPPOSITE

5. SOH CAH TOA Trigonometry Ratios Sine Ratio: SinѲ = Cosine Ratio:
Tangent Ratio:
TanѲ =
Opposite
Hypotenuse
Adjacent
Hypotenuse
Opposite
Adjacent
Hypotenuse
Hypotenuse
Adjacent
Opposite
Adjacent
Opposite
SOH
CAH
TOA

6. S O H C A T

7. Write down the value of Sin A, Cos A and Tan A
[5]
[3]
[4]

8. For each triangle calculate the value of , and4 3 5 5 7

9. Finding the value of the missing SIDE in Trigonometry
SOH CAH TOA
Opposite
Hypotenuse
10cm
sinѲ =
sin63 =
x = 10sin63
x = 8.91cm (2dp) x x 10
63o

10. Find the Value of the missing sidey 8m
49o

11. Find the Value of the missing side
[15]
500 x
SOHCAHTOA

12. Find the Value of the missing side
Given the triangle, we can work out the length of side a.
30°
7cm

13. Find the Value of the missing side
Given the triangle, can we work out the length of side b?
40°
15cm

14. Finding the value of the missing ANGLE in Trigonometry
Using the inverse trig buttons, Calculate:

15. Find the size of the missing Angle
SOH CAH TOA
Opposite
Hypotenuse
12m
sinѲ =
Ѳ = sin-1
Ѳ = 35.69o (2dp) 7m 7 12 Ѳ 7 12

16. Find the size of the missing Angle
Given the triangle, we can work out the angle .
13cm
9cm

17. Find the size of the missing Angle
Given the triangle, we can work out the angle .
29cm
To work out the size of angle , we know:
22cm

18. Find the size of the missing Angle
Given the triangle, we can work out the angle .
17cm
14cm

19. For each, find the size of the angle marked ?. .

20. THE ANGLE OF ELEVATION AND DEPRESSION
(a) Angle of depression = Angle looking down
(b) Angle of elevation = Angle looking up
depression
elevation

21. Angles of Elevation and Depression
Angles of Elevation: Angle of Depression:

22. Angles of Elevation How can I work out the height of the London Eye?
113.3m

23. Angles of Depression
I want to work out how far away the beach is from where I’m standing. I know I’m currently 53m above sea level.
21o
53m

24. Example 1
A plane takes off at an angle of 200 to the level ground. After flying for 100m how high is it off the ground.
100m
height
900
200

25. 14m
10m

27. Angles of Elevation and Depression
EXAMPLE 4: A boat is at sea and sees the light of a lighthouse in the distance. The captain knows the lighthouse is 86m tall. Given his angle of elevation when looking at the light is 13o, how far away is the boat from the lighthouse? EXAMPLE 5: While cleaning a hall, a cleaner spots a mouse on the floor 12m away. Given the woman is 1.6m tall, what is her angle of depression?