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

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

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

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 Angle Width Height then click Draw Use the calculator to check that the Sine of Angle equals the height and Cos Angle equals the width

Enter a value for Angle/Width/Height then click Draw 1.00 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 Enter Sin 20 on calculator to get height of a triangle with angle 20° sin-1 tan-1 cos-1 sin sin-1 cos cos-1 tan-1 tan SHIFT Ans On (-) √ ² x ÷ 6 7 8 9 0.5 + - Angle 30 Width 0.866 Height 1 2 3 4 5 = . Cos C Test Draw

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

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

Applying Trig to all triangles DEFINITIONS Opp Hyp = Opp 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

What is SohCahToa Opp Sin x° Hyp = Soh 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 H C H T H

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

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

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

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

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