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Trigonometry

Trigonometry. Measures of triangle. Remember Angles of triangle add to 180˚. Right-angled triangle. hypotenuse. opposite. adjacent. Use trig to solve triangles. Cah. cos x =. C. hypotenuse. a. b. opposite. x. A. B. c. adjacent. Cah. 12. cos x =. 13. C. 13. 5. x.

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Trigonometry

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

  2. Use trig to solve triangles Cah cos x = C hypotenuse a b opposite x A B c adjacent Cah 12 cos x = 13 C 13 5 x x = cos-1( 12/13) A B 12 x = 22.6

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

  4. 2.7 3 x = cos-1( ) 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? 3 m S o h C a h √ √ √ x 2.7 m 2.7 3 cos x = 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. Use your calculator : cos x˚ = 0.618 cos x˚ = 0.866 cos x˚ = 0.234 cos x˚ = 0.476 cos x˚ = 0.493 cos x˚ = 0.639 cos x˚ = 0.248 cos x˚ = 0.478 x ˚ = x ˚ = x ˚ = cos -1 ( ) x ˚ = x ˚ = x ˚ = cos-1 (0. 493) x ˚ = cos -1 ( x ˚ = cos 30˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = cos 69˚ = cos 47˚ = cos 23˚ = cos 54˚ = cos 62˚ = cos 73˚ = cos 78˚ = cos 90˚ = cos 4˚ =

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

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

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