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WHAT I LEARNED FROM CREATING AN ADVANCED TRIG CLASS DR. KATIE CERRONE THE UNIVERSITY OF AKRON COLLEGE OF APPLIED SCIENCE AND TECHNOLOGY

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BACKGROUND Technical College Our programs Accreditation Professional Exams Replaced Tech Calc II Advanced Trig Advanced Topics

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THE ADVANCED TRIG COURSE 1. Circles and Circular Curves : Arcs and central angles; Chords and segments, Secant and tangent lines,, Perpendicular bisectors; Lengths of tangent lines, chords, curves, external distances and middle ordinates; Circular curve computation 2. Parabolic Curves: Slope of a line (grade or gradient); Distance of a line; Points of vertical curvature, intersection, and tangency; Tangent elevations; Basic form of a parabola; Finding the external distance of a vertical curve 3. Spherical Trigonometry: Spherical triangles, Interior and dihedral angles; Sine formulas for spherical triangles; Cosine formulas for sides of spherical triangles; Cosine formulas for angles of spherical triangles; Applications of spherical triangles

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PARABOLIC CURVES

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Point of Curvature (PC): the beginning of the arc Point of Intersection (PI): The point where the two tangents intersect Point of Tangency (PT):The end of the arc Length of the Chord (L): The length from PC to PT PT PC PI L

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PARABOLIC CURVES PT PC PI L

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PARABOLIC CURVES PT PC PI L

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PARABOLIC CURVES PT PC PI L

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PARABOLIC CURVES PT PC PI = 452 ft. L = 6 -1.52.25

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PARABOLIC CURVES TURNING POINT PT PC PI = 452 ft. L

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PARABOLIC CURVES TURNING POINT PT PC PI = 452 ft. L = 6 -1.52.25

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CIRCULAR CURVES Point of Curvature (PC): the beginning of the arc Point of Intersection (PI): The point where the two tangents intersect Point of Tangency (PT):The end of the arc Length of the long chord (L): The length from PC to PT PT PC PI L

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CIRCULAR CURVES Tangent distance (T): The distance from PI to PC or from PI to PT Deflection Angle(Δ): The central angle of the angle at the Point of Intersection (PI) PT PC PI L T T RR Length of the Curve (C): the arclength from PC to PT Radius (R): Radius of the circle Degree of a Curve (D): the central angle that subtends a 100 foot arc

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CIRCULAR CURVES PT PC PI L T T RR

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CIRCULAR CURVES PT PC Δ/2 L/2 R

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CIRCULAR CURVES PT PC PI T T RR Δ/2

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CIRCULAR CURVES PT PC PI L T T RR

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CIRCULAR CURVES External Distance (E): The distance from the Point of Intersection to the middle of the curve Middle Ordinate (M): the length of the ordinate from the middle of the long chord to the middle of the arc PT PC PI L T T RR E M

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CIRCULAR CURVES PT PC PI L/2 T T RR E Δ/2

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CIRCULAR CURVES PT PC PI L/2 T T RR M Δ/2

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INCREASED TEST SCORES

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KATIE CERRONE kc24@uakron.edu The University of Akron College of Applied Science and Technology

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