Trigonometry Revision Booklet Name Introduction to Trigonometry Definition

Trigonometry Revision Booklet 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:

PYTHAGORAS THEOREM c a b a 2 +b 2 = c 2 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).

RIGHT ANGLED TRIANGLES HY TH EN US E 900 A ADJACENT OPPOSITE PO A HY PO TH EN U SE 900 OPPOSITE

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

S O H C A H T O A

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

For each triangle calculate the value of 5 4 3 5 7 , and

Finding the value of the missing SIDE in Trigonometry SOH CAH TOA 10 cm x 63 o Opposite sinѲ = Hypotenuse x sin 63 = 10 x = 10 sin 63 x = 8. 91 cm (2 dp)

Find the Value of the missing side y 8 m 49 o

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

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

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

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

Find the size of the missing Angle SOH CAH TOA 12 m 7 m Ѳ Opposite sinѲ = Hypotenuse 7 sinѲ = 12 7 -1 Ѳ = sin 12 Ѳ = 35. 69 o (2 dp)

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

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

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

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

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

Angles of Elevation and Depression Angles of Elevation: Angle of Depression:

Angles of Elevation 113. 3 m 50 o How can I work out the height of the London Eye?

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

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

14 m 10 m

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 86 m tall. Given his angle of elevation when looking at the light is 13 o, how far away is the boat from the lighthouse? EXAMPLE 5: While cleaning a hall, a cleaner spots a mouse on the floor 12 m away. Given the woman is 1. 6 m tall, what is her angle of depression?