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

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

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

PARABOLIC 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 Chord (L): The length from PC to PT PT PC PI L

PARABOLIC CURVES PT PC PI L

PARABOLIC CURVES PT PC PI L

PARABOLIC CURVES PT PC PI L

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

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

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

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

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

CIRCULAR CURVES PT PC PI L T T RR

CIRCULAR CURVES PT PC Δ/2 L/2 R

CIRCULAR CURVES PT PC PI T T RR Δ/2

CIRCULAR CURVES PT PC PI L T T RR

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

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

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

INCREASED TEST SCORES

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

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