TRIGONOMETRY

Trigonometry is the study of triangles.

Opposite Hypotenuse  Adjacent

Opposite Hypotenuse  Adjacent

Adjacent Hypotenuse  Opposite

Trigonometric Ratios The Ratio of the Opposite side and the Hypotenuse is called sine (or sin) The Ratio of the Adjacent side and the Hypotenuse is called cosine (or cos) Opposite Hypotenuse The Ratio of the Opposite side and the Adjacent side is called tangent (or tan)  Adjacent

Opp Sin  = Hyp Adj Cos  = Hyp Opp Tan  = Adj Hypotenuse Opposite  Adjacent Opp Adj Tan  =

Adj Hyp Cos  = sohcahtoa Opp Adj Opp Hyp Tan  = Sin  =

e.g. Find Sin , Cos  & Tan  Opp Hyp 21 29 Sin  = = Adj Hyp 20 29 29 m 21 m Adj Hyp 20 29 Cos  = =  20 m Opp Adj 21 20 Tan  = =

x x x x x e.g. If sin  = ½ , find . Opp Hyp Sin  = 1 2 20 = 20 x 1 2 m Sin  = x 1 2 20 =  x 20 m 20 x 1 2 x 20 = 20 x = 10 m

x x x x e.g. find the value of using your calculator. Opp Hyp Sin  = m Using a calculator sin 30˚ = 0.5 x x 8 8 x 0.5 = 30˚ 8 8 m x = 4 m

Opp Adj Opp Hyp Adj Hyp Tan  = Sin  = Cos  = Hypotenuse Opposite  Adjacent Opp Adj Opp Hyp Adj Hyp Tan  = Sin  = Cos  =

x x x x x e.g. find the value of using your calculator. Opp Hyp 8 m Sin 30˚ = Using a calculator, sin 30˚ = 0.5 x 30˚ 8 m x 8 8 x 0.5 = 8 x = 4 m

Opp Adj Opp Hyp Adj Hyp Tan  = Sin  = Cos  = Hypotenuse Opposite  Adjacent Opp Adj Opp Hyp Adj Hyp Tan  = Sin  = Cos  =

What do you do if the denominator is the missing side? e.g. x 30˚ 8

x x 8 Adj Opp Opp Tan  = Adj 8 Tan 30 = 30˚ 1. Identify the sides 2. Choose the trig ratio Opp Adj Tan  = 3. Substitute given values 8 x Tan 30 =

x x x x 8 0.5774 = 8 = 0.5774 = 13.86 4. Use calculator to find tan 30 5. Swap 0.5774 and x 8 = 0.5774 6. Solve x = 13.86

Opp Sin  = Hyp Adj Cos  = Hyp 15  9 If we know the lengths of any two sides in a right angle triangle, we can calculate the size of any angle in it e.g.1 1. Name the sides Opp Hyp Hyp Sin  = 15 2. Choose the correct trig ration Adj Hyp Cos  =  9 Adj

 Adj Cos  = Hyp 9 Cos  = 15 9  = Cos-1 15  = 53.13˚ 15  9 1. Name the sides 15 Hyp 2. Choose the correct trig ration Adj Hyp Cos  = 3. Enter the given data  9 15 Cos  = 9 Adj 4. Calculate the angle by using the “inverse ratio” button on the calculator. i.e. cos-1 9 15   = Cos-1  = 53.13˚

 Opp Sin  = Hyp 9 Sin  = 15 9  = Sin-1 15  = 36.87˚ 15  9 1. Name the sides 15 Hyp  2. Choose the correct trig ration Opp Hyp Sin  = 3. Enter the given data 9 15 Sin  = 9 Opp 4. Calculate the angle by using the “inverse ratio” button on the calculator. i.e. sin-1 9 15   = Sin-1  = 36.87˚

Opp Adj Opp Hyp Adj Hyp Tan  = Sin  = Cos  = Hypotenuse Opposite  Adjacent Opp Adj Opp Hyp Adj Hyp Tan  = Sin  = Cos  =