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Trigonometric Function Graphs. a A B C b c General Right Triangle General Trigonometric Ratios SOH CAH TOA.

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Presentation on theme: "Trigonometric Function Graphs. a A B C b c General Right Triangle General Trigonometric Ratios SOH CAH TOA."— Presentation transcript:

1 Trigonometric Function Graphs

2 a A B C b c General Right Triangle General Trigonometric Ratios SOH CAH TOA

3 a A B C b c a A B C b c Solutions for Non-Right Triangles Law of Sines Law of Cosines Two Examples of Non-Right Triangles

4 a A B C b c a A B C b c Solutions for Non-Right Triangles Law of Sines Law of Cosines These equations work no matter the type of triangle, acute, right, or obtuse.

5 The Unit Circle Radius = 1 Unit Length

6 Sine Graph -Parent function is an Odd Function, which means given an (x, y), (x, f(x)), on the graph there has to be a (– x, – y). Stated another way, given an f(x) then for ordered pairs (– x, – y) = (– x, f(– x) = (– x, – f(x))  sin(–  ) = – sin(  ). -Its period is 2 . -Since it is an Odd Function, it is symmetric about the origin. The Cosecant, the reciprocal of the Sine Function is also an Odd Function. -Domain - all Reals -Range [–1, 1] -It is positive in the First and Second Quadrant, and negative in the Third and Fourth Quadrant.

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8 Cosine Graph -Parent function is an Even Function, which means given an (x, y), (x, f(x)), on the graph there has to be a (– x, y). Stated another way, given an f(x) then for ordered pairs (– x, y) = (– x, f(– x) = (– x, f(x))  cos(–  ) = cos(  ) -Its period is 2 . -Since it is an Even Function, it is symmetric about the y-axis. The Secant, the reciprocal of the Cosine Function, is also an Even Function. -Domain - all Reals -Range [–1, 1] -It is positive in the First and Fourth Quadrant, and negative in the Second and Third Quadrant

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11 Cotangent Graph -Parent function is an Odd Function, which means given an (x, y), (x, f(x)), on the graph there has to be a (– x, – y). Stated another way, given an f(x) then for ordered pairs (– x, – y) = (– x, f(– x) = (– x, – f(x))  cot(–  ) = – cot(  ). -Its period is . -Since it is an Odd Function, it is symmetric about the origin. -Domain all Reals not to include multiples of  -Range All Reals -It is positive in the First and Third Quadrant, and negative in the Second and Fourth Quadrant.

12 Arc Functions

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14 Arccosine, cos –1, Function -It is the inverse function of the cosine, which means cos –1 (cos  ) =  and cos(cos –1 ½) = ½. -Domain [–1, 1] -Range [0,  ] - The value of the arccosine is an angle.

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16 END OF LINE


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