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SOH CAH TOA

SOH CAH TOA. Introduction. Angle. Side. Sin. Angle. Cos. Side. Angle. Side. Tan. Angle. Side. SCT. Six Example with choice. Find the angle. . . . . O. A. O. A. T. H. C. H. S. . . . . . . =. =. =. 7. =. b°. f°. =. =. 4. =. SHIFT. sin.

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SOH CAH TOA

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  1. SOH CAH TOA Introduction Angle Side Sin Angle Cos Side Angle Side Tan Angle Side SCT Six Example with choice

  2. Find the angle     O A O A T H C H S       = = = 7 = b° f° = = 4 = SHIFT sin cos tan cos-1 sin-1 tan-1 tan-1 sin-1 cos-1 Hyp Opp x ÷ (-) √ C ² 0 On + - 5 6 7 8 9 Adj . = 0 1 2 3 4 Ans Clear New Ex B

  3. Find the Side     O A O A T H C H S       H O SOH = Hyp Opp = = 13 = b 61° e = = = SHIFT sin cos tan cos-1 sin-1 tan-1 13xSin 61 tan-1 sin-1 cos-1 Hyp Opp x ÷ (-) √ C ² 11.37005619 On + - 5 6 7 8 9 Adj Sin . = 0 1 2 3 4 Ans Clear New Ex A

  4. Trigonometry and the Right Angle Triangle For every angle less than 90° a calculator can be used to find a unique value called its Sine Sin 9° = 0.1564… Sin 30° =0.5 Sin 83.7° = 0.1564… Height x° The calculator also gives unique values for the Cos and Tan of an angle Width In a RAT with a hypotenuse ( longest side ) of length 1 and an angle of 25° then The Sin 25° is the height, the Cos 25° is the width and the Tan 25° is a measure of how steep the hypotenuse is The next slide shows a RAT . You can enter a value into one of Height then click Draw Width Angle Use the calculator to check that the Sine of Angle equals the height and Cos Angle equals the width

  5. Enter a value for Angle/Width/Height then click Draw 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 Enter Sin 20 on calculator to get height of a triangle with angle 20° cos-1 tan-1 sin-1 0 sin cos-1 cos sin-1 tan-1 tan On SHIFT Ans x ÷ (-) √ ² 6 7 8 9 + - 0.5 Height 0.866 Width Angle 30 1 2 3 4 5 = . 0 Cos C Test Draw

  6. Hyp Hyp Sin 38° 1 4 =0.616 38° 38° Cos 38° =0.788 x x Hyp Hyp Calculate New Hypotenuse New Angle

  7. Definition Height ÷ ÷ Hyp Opp Hyp Sin x° Height x° =Height÷Hyp = Sin x° Adj Hyp Width Width =Width÷Hyp = Cos x° Hyp Cos x° x Hyp Compare to DST triangle. Can get a definition for Sin and Cos for ALL triangles.

  8. Applying Trig to all triangles DEFINITIONS Opp Opp = Hyp Sin x° Opp Hyp = Tan x° Adj Adj x° = Cos x° Hyp Adj You can use the above definitions to work out an angle in a RAT if you know two sides or You can work out a side if you know an angle and one of the remaining sides In a RAT the longest side is the HYPotenuse Hyp Opp Go across from the angle to find OPPosite x° The Adjacent is between the marked Angle and the right Angle Adj

  9. What is SohCahToa Opp = Sin x° Soh Hyp The next slides show you how to use SohCahToa Sin , Cos and Tan MUST be followed by an angle Adj = Cah Cos x° Hyp Opp = Tan x° Toa Adj O A O S C H H T H

  10. Using SohCahToa to find a side     O A O A T H C H S       SOH = Hyp Opp = b Opp Sin = 61° 13 = b Hyp 13 61° b 13 x Sin 61 11.37 = = = Identify sides then click letters in SohCahToa cos-1 sin-1 tan-1 tan-1 sin-1 cos-1 b on its own. Opposite of Div is mult

  11. Using SohCahToa to find a side    O A O A T H C H S       TOA = Opp = e Opp Tan = 51° = e Adj 12 51° e 12 x Tan 51 14.819 = = Adj 12 = Identify sides then click letters in SohCahToa cos-1 sin-1 tan-1 tan-1 sin-1 cos-1 Adj 51° No

  12. Using SohCahToa to find an angle    O A O A T H C H S       CAH = 5 ÷9 Hyp = 5 Adj 0.556 Cos = c° 9 = Hyp 9 c° c° Cos-1 (0.55556...) 56.3 = = Adj 5 = Move Cos to other side --- > Cos-1 SHIFT sin cos tan 5÷9 cos-1 sin-1 tan-1 Ans Ans tan-1 sin-1 cos-1 Opp x ÷ (-) √ C ² 0.55555556 56.2510114 On + - 5 6 7 8 9 No Adj . c° = 0 1 2 3 4 Ans

  13. a   9.37 13° b 25 b a 18 80   22° c    18.71 50 d d 6° 5.23 12° c e 90 6.89 f f e 17° 13.16 7 45 16° SHIFT sin cos tan cos-1 sin-1 tan-1 -6 tan-1 sin-1 cos-1 25 x ÷ (-) √ C ² All Sin 14 0 Next Six 5.676 x 10 On + - 5 6 7 8 9 . 6 Sides = 0 1 2 3 4 Ans A

  14. Trigonometry and the Right Angle Triangle For every angle less than 90° a calculator can be used to find a unique value called its Sine ….. Sin 30° = 0.5 Sin 9° = 0.1564…. Sin 83.7° = 0.1564… The calculator can also give a value for each angle called the Cos and also the Tan Cos 30° = 0.8660…… Cos 9° = 0.98768…. Cos 83.7° = 0.1097… Tan 30° = 0.5773…… Tan 9° = 0.1583…. Tan 83.7° = 9.0578… In a RAT with a hypotenuse ( longest side ) of length 1 and an angle of 25° then The Sin 25° is the height, the Cos 25° is the width and the Tan 25° is a measure of how steep the hypotenuse is

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