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Trigonomtery ,[object Object]
2.3 @ Foundation Level ,[object Object],- 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?!
At pass you must ,[object Object],-  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 and  solve problems involving these calculations
Calculate the area of a triangle ,[object Object],[object Object]
Sine and cosine rules to solve 2d problems ,[object Object]
What do you have to define? - sin  θ and cos  θ for  all values of  θ  tan  θ
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! AND Luckily for you I made you a present during the Snow Days cause I’m good like that!
Graphs of Trigonomteric Functions The 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.
Why study these graphs? ,[object Object],[object Object],[object Object],[object Object]
Graph of  y=sinx The function y = sinx may be graphed like any other function by taking different values for x and then finding the corresponding y - values . The table below shows angles between 0º and 360º and the value of the 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
[object Object],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]
[object Object],Using the same method graph  y =cos x  in the domain -180º≤ x ≤540º
I notice.. ,[object Object],[object Object]
off you go and try  y =tan x ,[object Object]
I think it’s.. ,[object Object],[object Object]
Graphs of Tan x  ,[object Object],[object Object],[object Object],[object Object],[object Object]
In Action ,[object Object]
Lets Interpret ,[object Object]
 
 
 
Interpreting graphs
 
 
 
 
 
 

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Trigonometry - Strand 3

  • 1.
  • 2.
  • 3.
  • 4.
  • 5.
  • 6. What do you have to define? - sin θ and cos θ for all values of θ  tan θ
  • 7. 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! AND Luckily for you I made you a present during the Snow Days cause I’m good like that!
  • 8. Graphs of Trigonomteric Functions The 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.
  • 9.
  • 10. Graph of y=sinx The function y = sinx may be graphed like any other function by taking different values for x and then finding the corresponding y - values . The table below shows angles between 0º and 360º and the value of the 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
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18.
  • 19.  
  • 20.  
  • 21.  
  • 23.  
  • 24.  
  • 25.  
  • 26.  
  • 27.  
  • 28.