MATH 145 – Applied Trigonometry

Course Coordinator

Alejandro Andreotti 

Catalog Description

MATH 145. Applied Trigonometry (2-1) Cr. 3 F.S. Prereq: Satisfactory performance on the placement exam, 2 years of high school algebra,1 year of high school geometry, or enrollment in MATH 140.Mathematical ideas regarding the conception of space. General Trigonometry, with an emphasis on the calculation of lengths, areas, and angles. The Law of Sines and the Law of Cosines. Polar, cylindrical, and spherical coordinate systems. Conic sections and Quadric Surfaces. Students in the College of Liberal Arts and Sciences may not count Math 145 toward the General education requirements. Only one of Math 143 and 145 may count toward graduation.


Trigonometry, Geometry, and the Conception of Space

Paul Tokorcheck

ISBN: 9781634871884


  • Module One: Definitions (3 weeks)

    • Lessons 1-5
  • Module Two: Applications (4 weeks)

    • Lessons 6-11
  • Module Three: Coordinate Systems (3 weeks)

    • Lessons 12-16
  • Module Four: Conics (3 weeks)

    • Lessons 17-20
  • Module Five: Quadrics (3 weeks)

    • Lessons 21-24



  • Understand general definitions regarding sets, particularly sets of numbers.
  • Distinguish between integers, rational numbers, and irrational numbers.
  • Use units of measure and convert between units, using dimensional analysis.
  • Understand both radian and degree measures and how to translate between them.
  • Know the six trigonometric ratios. Be able to evaluate trigonometric ratios using both a calculator and the Unit Circle.
  • Given data about a right triangle, be able to find any missing side lengths or angles.


  • Understand concepts relating to functions, such as their domains, ranges, and whether or not they are one-to-one.
  • Know the six inverse-trigonometric functions. Be able to evaluate trigonometric ratios using both a calculator and the Unit Circle.
  • Be able to solve equations relating an unknown angle, either for a unique solution or over interval.
  • Use basic trigonometric identities, such as the Sum/Difference Formulas, the Law of Sines, and the Law of Cosines, to help solve equations.
  • Construct and solve equations for a variety of real-world examples.
  • Be able to find unknown side lengths or angles for general triangles.


  • Use Polar Coordinates to describe points or equations in two dimensions, and convert between them and rectangular coordinates.
  • Use Cylindrical Coordinates to describe points or equations in three dimensions, and convert between them and rectangular coordinates.
  • Use Spherical Coordinates to describe points or equations in three dimensions, and convert between them and rectangular coordinates.
  • Be able to graph sinusoidal curves, and identify features such as amplitude and period.
  • Manipulate the sine function and its graph using transformations of the plane.


  • Recognize the graphs and equations of parabolas, ellipses, and hyperbolas.
  • Complete the square to put quadratic equations into standard forms.
  • Analyze the equations of conics to identify features such as foci and vertices. Modify a given conic section using graph transformations.


  • Use level curves to describe general surfaces in R3.
  • Be able to both identify and generate surfaces of rotation and their features.
  • Recognize the graphs and equations of cones, ellipsoids, paraboloids, and hyperboloids in R3.
  • Be able to sketch a given quadric surface and its intersection with specified horizontal and vertical planes.

Free Expression Statement

Iowa State University supports and upholds the First Amendment protection of freedom of speech and the principle of academic freedom in order to foster a learning environment where open inquiry and the vigorous debate of a diversity of ideas are encouraged. Students will not be penalized for the content or viewpoints of their speech as long as student expression in a class context is germane to the subject matter of the class and conveyed in an appropriate manner.

Students With Disabilities

Iowa State University is committed to assuring that all educational activities are free from discrimination and harassment based on disability status. Students requesting accommodations for a documented disability are required to work directly with staff in Student Accessibility Services (SAS) to establish eligibility and learn about related processes before accommodations will be identified. After eligibility is established, SAS staff will create and issue a Notification Letter for each course listing approved reasonable accommodations. This document will be made available to the student and instructor either electronically or in hard-copy every semester. Students and instructors are encouraged to review contents of the Notification Letters as early in the semester as possible to identify a specific, timely plan to deliver/receive the indicated accommodations. Reasonable accommodations are not retroactive in nature and are not intended to be an unfair advantage. Additional information or assistance is available online at, by contacting SAS staff by email at, or by calling 515-294-7220. Student Accessibility Services is a unit in the Dean of Students Office located at 1076 Student Services Building.