Junior Cert TRIGONOMETRY

Some considerations Make sure the calculator is in Degree Mode (DRG button) Practice getting the sine/cos/tan of various angles Inverse functions: [2nd F button] Use of backets is important when finding inverses: e.g Some notes for each bullet in turn: This is the first crucial step that has to be carried out before any trig work occurs This is to enable pupils to get a ‘feel’ for using these new buttons Explain that 2nd F button puts the calculator into inverse mode. So if we have a ratio, we must use 2nd F to find the angle.

SECTION 1 RIGHT ANGLED TRIANGLES

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

a2 +b2 = c2 PYTHAGORAS THEOREM c a b The square of the hypotenuse is equal to the sum of the squares on the other 2 sides. This theorem is used when you are looking for the length of one side of a triangle when you are given the measurements of the other 2 sides. ( Remember this theorem only works for right angled triangles).

Hypotenuse [H]

Hypotenuse [H] Opposite [O] A Adjacent [A]

A Hypotenuse [H] Adjacent [A] Opposite [O]

SOHCAHTOA Cosine A Cos A = H [H] [O] Sine O Sin A = H A Tangent [A] O Tan A = SOHCAHTOA

[5] [3] [4] [H] [O] A [A] O 3 SOHCAHTOA Sin A = = H 5

[5] A [3] [4] [H] [O] [A] A 4 SOHCAHTOA Cos A = = H 5

[5] A [4] [O] [H] [3] [A] O 3 SOHCAHTOA Tan A = = A 4

[13] A [12] [5] [H] [O] [A] O 12 SOHCAHTOA Sin A = = H 13

[13] A [12] [5] [H] [O] [A] A 5 SOHCAHTOA Cos A = = H 13

[13] A [12] [5] [H] [O] [A] O 12 SOHCAHTOA Tan A = = A 5

O SOHCAHTOA H Looking for x [15] 300 x Given [H] [O] O x Sin 300 = = H 0.5 1 = [A] SOHCAHTOA x = 15(0.5) = 7.5

SOHCAHTOA O A Looking for x [15] 500 x Given [H] [O] O x tan 50o = = A 1.1917 1 = [A] SOHCAHTOA x = 15(1.1918) = 17.876

SOHCAHTOA H A Looking for x [15] 35o 16’ x Given A 15 [H] Cos 35o 16’ = = [O] H x Cos 35o 16’ = 0.8164 15 x 0.8164 1 = [A] x(0.8165) = 15 SOHCAHTOA 15 x = = 18.37 0.8165

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

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

100m HYP opp height 900 200 In this we are given the Hyp. And we are looking for the Opp So we use the Sin Formula

14m 10m

10m 8m

Note: If given ratio always draw right angled triangle Adj = 5 Hyp = 13 x