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Trigonometry

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Trigonometry

  1. 1. TRIGONOMTERY Ms. Carter
  2. 2. 2.3 @ FOUNDATION LEVELYou should be able to.. - solve problems that involve finding heights and distances from right-angled triangles (2D only) − use of the theorem of Pythagoras to solve problems (2D only) − solve problems that involve calculating the cosine, sine and tangent of angles between 0 and 90
  3. 3. 2.3 @ FOUNDATION LEVELYou should be able to.. - solve problems that involve finding heights and distances from right-angled triangles (2D only) − use of the theorem of Pythagoras to solve problems (2D only) − solve problems that involve calculating the cosine, sine and tangent of angles between 0 and 90 THIS YOU CAN DO!!!! RIGHT?!
  4. 4. AT PASS YOU MUSTbe able to...- use trigonometry to calculate the area of a triangle− use the sine and cosine rules to solve problems (2D)− define sin θ and cos θ for all values of θ− define tan θ− calculate the area of a sector of a circle and the length of an arc andsolve problems involving these calculations
  5. 5. CALCULATE THE AREA OF A TRIANGLEYou can do this by using the ‘Sine Rule’.And Or the Area of a Triangle Formula 1/2ab sin C.
  6. 6. SINE AND COSINE RULES TO SOLVE 2D PROBLEMSCosine Rule a² = b² + c² - 2bc cos A
  7. 7. WHAT DO YOU HAVE TO DEFINE?- sin θ and cos θ forall values of θ- tan θ
  8. 8. LASTLYcalculate the area of a sector of a circle and the length of an arc and solve problems involving these calculations
  9. 9. LASTLY calculate the area of a sector of a circle and the length of an arc and solve problems involving these calculations For the moment that is ALL the Pass Material! ANDLuckily for you I made you a present during the Snow Days cause I’m good like that!
  10. 10. GRAPHS OF TRIGONOMTERIC FUNCTIONSThe Maths LC Syllabus 2010/11 says that: Students working at LC HL should be able to - graph trigonometric functions of type aSin nx , aCos nx for a, n ∈ N.
  11. 11. WHY STUDY THESE GRAPHS?Most commonly used graphs in statistics andengineering.They are used for modelling many different naturaland mechanical phenomena (popultions, acoustics).You must be able to graph Periodic Graphs. Theseare graphs that the shape repeats itselve after acertain amount of time.Anything that has a regular cycle(like tides, rotation ofthe earth) can be modelled using a sine or cosinecurve.
  12. 12. GRAPH OF Y=SINXThe function y = sinx may be graphed like any other function by taking differentvalues for x and then finding the corresponding y - values.The table below shows angles between 0º and 360º and the value ofthe sine ❨y-value❩ of each of these angles x= 0º 45º 90º 135º 180º 225º 270º 315º 360º y = sinx 0 0.7 1 0.7 0 -0.7 -1 -0.7 0
  13. 13. If the values of x are extended through another fullrotation of 360º or - 360º, the values of sinx arerepeated for each full rotation of 360º (or 2π) From this grpah it can be seen that the values of sine x repeat themselves every 360º. The highest y-value of the graph is 1 and the lowest is -1. Thus the range of the function is [-1,1]
  14. 14. USING THE SAME METHOD GRAPH Y=COSX IN THE DOMAIN -180º≤X≤540º What do you notice about this graph?
  15. 15. I NOTICE..It’s a periodic graph with a period of 360º.The range is also [-1,1].
  16. 16. OFF YOU GO AND TRY Y=TANX Whats different about this graph?
  17. 17. I THINK IT’S..It repeats itself every 180º or pi.O! and there are two vertical asymptotes at x = 90ºand at x = 270º.
  18. 18. GRAPHS OF TAN XThere are uncommon but they do occur inengineering and science problems.Remember that tan x = sinx/cosx and for somevalues of x cosx has value 0.For example x = π/2 and x = 3π/2.When this happens we have 0 in the denominator of thefraction and this means it is undefined.So there will be a gap in the curve and this gap is called adiscontinuity.
  19. 19. IN ACTIONhttp://www.intmath.com/trigonometric-graphs/4-graphs-tangent-cotangent-secant-cosecant.php
  20. 20. LETS INTERPRETy = tan x
  21. 21. INTERPRETING GRAPHS

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