Trigonometry - step by step

Copyright Barbara Edwards 2005 soh cah toa TRIGONOMETRY Copyright Barbara Edwards 2005 Sine, tangent and cosine are really about curves Sine and cosine curves form waves – they are important in the physics of soundCopyright Barbara Edwards 2005 But we are going to use sine, tangent and cosine (sin, tan, cos) To work out SIDES and ANGLES in RIGHT ANGLED TRIANGLESCopyright Barbara Edwards 2005See a right angled triangle Think Soh cah toa (1 angle, 2 sides) And PYTHAGORAS (3 sides) Know 2/3, find the 3rdCopyright Barbara Edwards 2005 Soh cah toa Step 1 Label the TWO sides Soh cah toa is about three things, one angle and two sides, You will be given 2, asked to find the third The labels are HYPOTENUSE H ADJACENT A OPPOSITE 0Copyright Barbara Edwards 2005 Step 1 Label the TWO sides The HYPOTENUSE is always across the way from the right angle Remember Pythagoras? It will always be the longest side HYPOTENUSE H HCopyright Barbara Edwards 2005 Step 1 Label the TWO sides xo Opposite OTo angle x Adjacent A To angle xCopyright Barbara Edwards 2005 xo Opposite Oto angle x But Adjacent A to angle y Adjacent A to angle x But Opposite O to angle y y0 Adjacent and Opposite relates to the AngleCopyright Barbara Edwards 2005 Label the 2 sides marked (1) and (2) Use just the letters, A, O and HCopyright Barbara Edwards 2005 Answers to exercise 8th H O7th O H6th O A5th A H4th O H3rd A O2nd H A1st O H(1) (2)Copyright Barbara Edwards 2005 Step 2 Decide what you want to use Sin (short for sine) Tan (short for tangent) Cos (short for cosine) If you have only labelled two sides, ones that have been given to you or you have been asked to find, you can use the two letters SOH CAH TOA O and H use sin, A and H use cos, O and A use tan Use the answer to the last exercise labelling 2 sides and add sin, tan or cosCopyright Barbara Edwards 2005 Answers to exercise 8th H O Sin 7th O H Sin 6th O A Tan 5th A H Cos 4th O H Sin 3rd A O Tan 2nd H A Cos 1st O H Sin (1) (2)Copyright Barbara Edwards 2005 Step 3: The Calculation Use the ‘helper’ You may want to make a page of them for reference and put them in your maths kit But if you are coming up to an exam or test, write them out each time to help you to remember themCopyright Barbara Edwards 2005 Step 3: The Calculation THE HELPER O sin H A cos H O tan ACopyright Barbara Edwards 2005 Step 3 The Calculation Write what you have got to find Like O = O ? 360 8.2 cmsCopyright Barbara Edwards 2005 Step 3 The Calculation O = O tan A O ? 360 8.2 cms We are finding O Put your finger on O The two at the bottom means multiply O = tan x A Put in the numbers O = tan 36 x 8.2 O = 5.8 to 1 dpCopyright Barbara Edwards 2005 Step 3 The Calculation – another problem H = O sin H 10 360 We are finding H Put your finger on H The two others, O is above the line and sin below so DIVIDE H = O/sin Put in the numbers H = 10/sin 36 H = 17.01 to 2 dp H ?Copyright Barbara Edwards 2005 Questions 1 to 12