1. M May Trigonometry Measures of triangle Remember Angles of triangle add to 180˚ hypotenuse opposite adjacent Right-angled triangle

2. M May x A B C a b c Cah hypotenuse adjacent opposite A C B 5 12 13 x cos x = 12 13 Cah x = cos -1 ( 12 / 13 ) x = 22.6

3. M May cos 60˚ = cos 30˚ = cos 45˚ = cos 15˚ = cos 0˚ = cos 90˚ = 0.5 0.866 0.707 0.966 1 0 cos 10˚ = cos 20˚ = cos 35˚ = cos 80˚ = cos 40˚ = 0.985 0.940 0.819 0.174 0.766 cos x ˚ = 0.5 x ˚ = cos -1 (0.5) x ˚ = 60˚ cos x ˚ = 0.8 x ˚ = cos -1 (0.8) x ˚ = 36.9˚ cos x ˚ = 0.65 cos x ˚ = 0.12 cos x ˚ = 0.83 cos x ˚ = 0.21 cos x ˚ = 0.33 cos x ˚ = 0.47 cos x ˚ = 0.05 cos x ˚ = 0.72 x ˚ = cos -1 (0.65) x ˚ = cos -1 (0.12) x ˚ = cos -1 (0.83) x ˚ = cos -1 (0.21) x ˚ = cos -1 (0.33) x ˚ = cos -1 (0.47) x ˚ = cos -1 (0.05) x ˚ = cos -1 (0.72) x ˚ = 49.5˚ x ˚ = 83˚ x ˚ = 34˚ x ˚ = 78˚ x ˚ = 71˚ x ˚ = 62˚ x ˚ = 87˚ x ˚ = 44˚

4. M May The angle a ramp makes with the horizontal must be 23 ± 3 degrees to be approved by the Council. If this ramp is 4m long and is placed 2.7 metres from the step, will it be approved? 2.7 m 3 m x S o h C a h √√ cos x = 2.7 3 x = cos -1 () 2.7 3 x = 25.84193276 x = 25.8˚ So since the angle lies between 20˚ and 26˚ the Council would approve the ramp.20˚ < 25.8˚ < 26˚ √

5. M May cos 30˚ = Use your calculator : cos 69˚ = cos 47˚ = cos 23˚ = cos 54˚ = cos 62˚ = cos 73˚ = cos 78˚ = cos 90˚ = cos 4˚ = cos x ˚ = 0.493 x ˚ = cos -1 (0. 493) x ˚ = cos x ˚ = 0.639 x ˚ = cos -1 ( ) x ˚ = cos x ˚ = 0.248 x ˚ = cos -1 ( x ˚ = cos x ˚ = 0.478 x ˚ = cos x ˚ = 0.866 x ˚ = cos x ˚ = 0.234 x ˚ = cos x ˚ = 0.618 x ˚ = cos x ˚ = 0.476 x ˚ =

6. M May cos 30˚ = Use your calculator : cos 69˚ = cos 47˚ = cos 23˚ = cos 54˚ = cos 62˚ = cos 73˚ = cos 78˚ = cos 90˚ = cos 4˚ = cos x ˚ = 0.493 x ˚ = cos -1 (0. 493) x ˚ = cos x ˚ = 0.639 x ˚ = cos -1 ( ) x ˚ = cos x ˚ = 0.248 x ˚ = cos -1 ( x ˚ = cos x ˚ = 0.478 x ˚ = cos x ˚ = 0.866 x ˚ = cos x ˚ = 0.234 x ˚ = cos x ˚ = 0.618 x ˚ = cos x ˚ = 0.476 x ˚ = 0.866 0.358 0.682 0.921 0.588 0.469 0.292 0.208 0 0.998 60.5˚ 0.639 50.3˚ 0.248) 75.6˚ cos -1 (0.478) 61.4˚ cos -1 (0.866) 30˚ cos -1 (0.234) 76.5˚ cos -1 (0.618) 51.8˚ cos -1 (0.476) 61.6˚

7. M May Remember The cosine of an angle is found using C a h cos x = x A djacent h ypotenuse x 9 15 12 cos x = 12 15 x = cos -1 (12/15) x = 36.9˚ S o h C a h T o a