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:

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).

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

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

S O H C A T

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

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

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

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

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

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

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

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 Opposite Hypotenuse 12m sinѲ = Ѳ = sin-1 Ѳ = 35.69o (2dp) 7m 7 12 Ѳ 7 12

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

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

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

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 How can I work out the height of the London Eye? 113.3m

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

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

14m 10m

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?