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xyr definitions - 1.3 The xyr Definitions of the...

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1.3: The xyr Definitions of the Trigonometric Functions The six trigonometric functions can be defined in several ways. The first way may be referred to as the xyr definitions, where x and y are the coordinates of a point on the terminal side of the angle when placed in standard position, and r is the distance of that point from the origin. The inputs to the functions will be angles, and the outputs will be ratios of the numbers x, y, and z. Ex : Given that P (3,5) = , compute values for the six trigonometric functions of the angle in standard position. First we compute r : 2 2 r 3 5 r 9 25 r 34 = + = + + = We can now write down these ratios, given that we already know that x 3 = and y 5 = . Place θ in standard position, pick any point on the terminal side of θ except the origin itself, and use the coordinates of this point to compute its distance from the origin. 2 2 r x y , r 0 = + > = + > + + We define the six trigonometric functions as follows. (sine, cosine, tangent, cotangent, secant, cosecant) y sin r x cos r y tan , x 0 x x cot , y 0 y r sec , x 0 x r csc , y 0 y θ = θ =
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