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Trigonometry

Trigonometry. Right angled triangles. A triangle. Opposite and Adjacent are relative to the angle. The 4cm side is opposite to A The 6cm side is adjacent to A The 6cm side is opposite to B The 4cm side is adjacent to B. SOH CAH TOA Sine, Cosine & Tangent of an angle. SOH CAH TOA. SOH

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Trigonometry

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  1. Trigonometry Right angled triangles

  2. A triangle

  3. Opposite and Adjacent are relative to the angle • The 4cm side is opposite to A • The 6cm side is adjacent to A • The 6cm side is opposite to B • The 4cm side is adjacent to B

  4. SOH CAH TOASine, Cosine & Tangent of an angle

  5. SOH CAH TOA • SOH • Some Old Houses • (Sine of angle =Opposite side / Hypotenuse) • CAH • Creak And Howl • (Cosine of angle = Adjacent side / hypotenuse) • TOA • Through Out Autumn • (Tangent of angle = Opposite side / adjacent side)

  6. TOA SOH CAH • TOA • Tom’s Old Auntie • Tangent of angle = Opposite side / adjacent side • SOH • Sat On Him • Sine of angle =Opposite side / Hypotenuse • CAH • Cursing At Him • Cosine of angle = Adjacent side / hypotenuse

  7. SOH CAH TOA • SOH S O H Opposite side = sin (x) times hypotenuse Hypotenuse = opposite side divided by sin (x) Sin (x) = opposite side divided by hypotenuse

  8. SOH CAH TOA C A • CAH H Adjacent side = cos (x) times hypotenuse Hypotenuse = adjacent side divided by cos (x) Cos (x) = adjacent side divided by hypotenuse

  9. SOH CAH TOA A • TOA T O Opposite side = tan (x) times adjacent side Adjacent side = opposite side divided by tan (x) tan (x) = opposite side divided by adjacent side

  10. Problems for trig A stage, is to be built for a concert, it has to be 2m high so the audience can see the show. The equipment needs to be pushed up onto the stage. Health and safety rules say that a ramp must have a slope of no more than 15 degrees. The crew need to work out how far away from the stage to start building the ramp. m

  11. A stage, is to be built for a concert, has to be 2m high so the audience can see the show. The equipment needs to be pushed up onto the stage. Health and safety rules say that a ramp must have a slope of no more than 15 degrees. The crew need to work out how far away from the stage to start building the ramp. m

  12. Put answer in context: The ramp must start from at least 7.5m away from the stage

  13. From take-off, an aeroplane climbs at an angle of 20o. When the aeroplane has flown 10km, what height has it reached? km Distance from ground.

  14. Looking for opposite (distance from ground) got hypotenuse. Must be Sine formula triangle km Distance from ground. Distance from ground = sin (20) x 10 = 3.42 km from the ground

  15. A plane flies 300km on a bearing of 132 0 from an airport. How far south and east is it from the airport. Give answer correct to 3 s.f. North is always straight up your page for these questions.. Bearings are always measured from north around in a clockwise direction.

  16. Draw the problem and work out the angle at AThen choose which side you want to find first then choose the formula triangle to suit.

  17. Distance South firstlooking for adjacent side therefore use cosine formula triangle

  18. Distance East looking for opposite side therefore use the sine formula triangle

  19. Ratio just means the number you get when you divide one number by another Similar shapes have the same angles – so they have the same angle ratios. Sin(30) is always the same number no matter what size the opp or hyp A Cos(30) is always the same number no matter what size the adj or hyp A1 A2 Tan(30) is always the same number no matter what size the opp or adj B C C1 C2

  20. Sine ratioSin(x)=opp / hyp 4.3 / 8.42 = ?

  21. To find the angle (x) when you know sin (x) use the calculator inverse sine function (sin-1) • Sin (x) = 0.86 x = Sin-1 (0.86) = 59 0 • Sin (x) = 0.35 x = Sin-1 (0.35) = 21 0 Sin (x) = 0.45 , what is x ? Sin (x) = 0.91, what is x? 27 0 66 0

  22. Cosine ratiocos(x) = adj / hyp Cos(30) = 0.86 16/18.46=?

  23. To find the angle (x) when you know cos (x) use the calculator inverse cosine function (cos-1) • Cos (x) = 0.86 x = Cos-1 (0.86) = 31 0 • Cos (x) = 0.35 x = Cos-1 (0.35) = 70 0 Cos (x) = 0.45 , what is x ? Cos (x) = 0.91, what is x? 63 0 24 0

  24. Tangent ratiotan(x) = opp / adj Tan(30) =0.58 7.58 / 13 = ?

  25. To find the angle (x) when you know tan (x) use the calculator inverse tangent function (tan-1) • tan (x) = 0.86 x tan(0.86) = 41 0 • tan (x) = 0.35 x = tan-1 (0.35) = 19 0 tan (x) = 0.45 , what is x ? tan (x) = 0.91, what is x? 24 0 42 0

  26. A tourist lift to the top of a cliff travels 23m from ground to the top of the cliff. The height from ground to the top of the cliff is 20m what is the angle of elevation? Choose a formula triangle Sketch the problem We have opposite and hypotenuse must be sine formula triangle

  27. Looking for the angle BAC.Work out the sine of the angle BAC then use inverse sine to get angle.

  28. Health and Safety stipulates that a ladder held up at the side of a wall must have an angle of elevation between 700 and 800 to be considered safe. The height to be reached is 2.4m but the only ladder available is 4.9m will it be classed as safe? Not safe

  29. Find angles A and B?We know all sides so ANY formula triangle will be ok to use.

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