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5.7 – Sketching the Reciprocal Trigonometric Functions Recall the reciprocal graphing techniques used for sketching rational functions like the reciprocal linear and the reciprocal quadratic functions from unit #2. Ex. if y = f(x) then y = 1/f(x) The same technique can be used to sketch the reciprocal trigonometric functions. f(x) = sin θ g(x) = cos θ 10 10 10 5 5 5 −π π 2π 3π 4π −π −5 csc = cosecant π 2π 3π 4π −π −5 sec = secant −10 π cot = cotangent sec θ = 1/cos θ 10 5 5 5 2π 3π 4π 4π 3π 4π cot θ = 1/tan θ 10 π 3π −10 10 −π 2π −5 −10 csc θ = 1/sin θ Note that these sketches are to give one a general idea of the shape and are not exact as have stretch factors. h(x) = tan θ −π π 2π 3π 4π −π π −5 −5 −5 −10 −10 −10 2π Use the accompanying sheets to accurately sketch the reciprocal trigonometric functions. Once sketched describe the period, amplitude, domain, range, increasing and decreasing intervals in the table below; Function sin θ Increasing Decreasing csc θ cos θ sec θ tan θ cot θ 5.7 – sketching the reciprocal trigonometric functions Domain Range Period Amplitude 5.7 – Sketching the Reciprocal Trigonometric Functions Investigation Sheet Have your sketches from section 5.4 on top of these functions so you can take the reciprocal of them. Reciprocal Trigonometric Functions using degrees 1) f(x) = csc θ 8 Add decimal to make y-axis from -1 to 1 6 4 2 −270 −180 −90 90 180 270 360 450 540 630 720 90 180 270 360 450 540 630 720 90 180 270 360 450 540 630 720 −2 −4 −6 −8 10 2) g(x) = sec θ 8 6 4 2 −270 −180 −90 −2 −4 −6 −8 10 3) h(x) = cot θ 8 6 4 2 −270 −180 −90 −2 −4 −6 −8 10 5.7 – sketching the reciprocal trigonometric functions 5.7 – Sketching the Reciprocal Trigonometric Functions Investigation Sheet Basic Trigonometric Functions using radians 1) f(x) = csc x 2) g(x) = sec x 3) h(x) = cot x 5.7 – sketching the reciprocal trigonometric functions