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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. Toa. tan x =. C. hypotenuse. a. b. opposite. x. A. B. c. adjacent. Toa. 5. tan x =. 12. 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 Toa tan x = C hypotenuse a b opposite x A B c adjacent Toa 5 tan x = 12 C 13 5 x x = tan-1( 5/12) A B 12 x = 22.6

  3. tan x˚ = 1 tan x ˚ = 0.8 tan 45˚ = 1 x˚ = tan -1 (1) x˚ = tan-1 (0.8) tan 30˚ = 0.577 x˚ = 45˚ x˚ = 38.7˚ tan 60˚ = 1.732 tan 15˚ = 0.278 tan x˚ = 0.5 tan x˚ = 0.33 x˚ = tan-1 (0.5) x˚ = tan-1 (0.33) tan 0˚ = 0 x˚ = 26.6˚ x˚ = 18.3˚ tan x˚ = 0. 12 tan x˚ = 0.47 tan 80˚ = 5.67 x˚ = tan-1 (0.12) x˚ = tan-1 (0.47) tan 85˚ = 11.43 x˚ = 6.8˚ x˚ = 25.2˚ tan x˚ = 0.83 tan x˚ = 0.05 tan 88˚ = 28.64 x˚ = tan-1 (0.83) x˚ = tan-1 (0.05) x˚ = 2.9˚ x˚ = 39.7˚ tan 35˚ = 0.700 tan x˚ = 0.21 tan x˚ = 0.72 tan 87˚ = 19.08 x˚ = tan-1 (0.21) x˚ = tan-1 (0.72) x˚ = 11.9˚ x˚ = 35.8˚ tan 22˚ = 0.404

  4. 1.3 2.9 x = tan-1( ) The angle a ramp makes with the horizontal must be 23 ± 3 degrees to be approved by the Council. If this ramp lifts to top of the step 1.3 m high and is placed 2.9 metres from the step, will it be approved? S o h C a h T o a √ √ √ √ 1.3 m 1.3 2.9 x tan x = 2.9 m x = 24.14554196 x = 24.1˚ So since the angle lies between 20˚ and 26˚ the Council would approve the ramp. 20˚ < 24.1˚ < 26˚

  5. Use your calculator : tan x˚ = 0.618 tan x˚ = 0.866 tan x˚ = 0.234 tan x˚ = 0.476 tan x˚ = 0.493 tan x˚ = 0.639 tan x˚ = 0.248 tan x˚ = 0.478 x ˚ = x ˚ = x ˚ = tan -1 ( ) x ˚ = x ˚ = x ˚ = tan -1 (0. 493) x ˚ = tan -1 ( x ˚ = tan 30˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = tan 69˚ = tan 47˚ = tan 23˚ = tan 54˚ = tan 62˚ = tan 73˚ = tan 78˚ = tan 89˚ = tan 4˚ =

  6. Use your calculator : tan x˚ = 0.618 tan x˚ = 0.639 tan x˚ = 0.493 tan x˚ = 0.478 tan x˚ = 0.234 tan x˚ = 0.866 tan x˚ = 0.476 tan x˚ = 0.248 x ˚ = x ˚ = x ˚ = tan -1 (0. 493) x ˚ = tan -1 ( x ˚ = x ˚ = tan -1 ( ) x ˚ = x ˚ = tan 30˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = x ˚ = tan 69˚ = tan 47˚ = tan 23˚ = tan 54˚ = tan 62˚ = tan 73˚ = tan 78˚ = tan 89˚ = tan 4˚ = tan -1(0.866) 0.577 26.2˚ 40.89˚ 2.605 1.072 0.639 tan -1(0.234) 32.6˚ 13.2˚ 0.424 1.38 0.248) tan -1(0.618) 1.88 13.9˚ 31.7˚ 3.27 4.705 57.29 tan-1(0.478) tan -1(0.476) 25.5˚ 25.5˚ 0.070

  7. Remember T o a The tangent of an angle is found using opposite tan x = x Adjacent 9 tan x = 15 9 12 x 12 x = tan-1(9/12) x = 36.9˚

  8. S o h C a h T o a Hypotenuse Opposite x Adjacent ah o h o a S C T Opposite Adjacent Opposite sinx = cosx = tanx = Hypotenuse hypotenuse Adjacent

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