Trigonometry and Analytical Geometry—from the Greek words for “triangle measure”—is the branch of mathematics that deals with the measurement and calculation of triangles. . It is a prerequisite for the study of advanced mathematics (e.g., calculus). Its principles are used in such fields as surveying, navigation, astronomy, and civil, mechanical, electrical, and sound engineering. Analytical (or Analytic) Geometry is designed to represent space through the use of numbers and algebra, with points in space represented by ordered sets of numbers.
Course Description
The course has seven study units—Plane Trigonometry and Analytical Geometry, Parts 1 – 5, and Analytical Geometry, Parts 1 and 2—with numerous practice problems (and answers) plus seven exams. There are two supplements: Logarithms and Trigonometric Tables.
Also included: Answer Key Supplement, with solutions to the Practice Exercise problems in the study units.
Course Objectives
Upon completion of this course, students will be able to:
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Find the unknown parts of a triangle (“solve the triangle”)
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Solve a variety of mathematical problems easily and quickly
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Define angles, sides, Pythagorean theorem, trigonometric functions, and other terms
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Use the table of natural trigonometric functions
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Use interpolation to find the functions of an angle that is measured to seconds
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Round off numbers correctly, replacing dropped digits with zeros
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Accurately measure angles in either radians or degrees
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Know and use letters of the Greek alphabet when naming angles
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Explain the difference between an equation and an identity
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Express the functions of any angle
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Understand logarithms and use the table of log functions
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Realize the value of orderly work when solving trig problems
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Explain the law of cosines, the law of tangents, and Mollweide’s equations
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Accurately plot graphs of trigonometric functions
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Discuss the methods used in analytical geometry to solve problems
Course Outline
Study Unit 1: Plane Trigonometry and Analytical Geometry, Part 1
Introduction; Trigonometry and Analytical Geometry Defined; What It Deals With; Why We Study It; Solving a Triangle; Trigonometric Functions; How to Find Them; How to Use the Table of Natural Trigonometric Functions; Interpolation; Approximate Numbers; Significant Figures; Rounding Off Numbers; Pythagorean Theorem
Study Unit 2: Plane Trigonometry and Analytical Geometry, Part 2
Introduction; Angles; How to Measure Angles; Rectangular Coordinates; Angles in Standard Position; Quadrantal and Coterminal Angles; Signs of Trigonometric Functions; Finding Values of Functions of Certain Angles; Trigonometric Identities; Expressing All Functions in Terms of One Function; Using the Greek Alphabet
Study Unit 3: Plane Trigonometry and Analytical Geometry, Part 3
Introduction: Expressing Functions of Any Angle; Application of Reduction Formulas; Logarithm Defined; Why We Use Logarithms; How to Use Table of Log Functions; Basic Facts Concerning Logarithms; Importance of Orderly Work; Solving Right Triangles by Using Logarithms; Types of Oblique Triangles; Law of Cosines
Study Unit 4: Plane Trigonometry and Analytical Geometry, Part 4
Introduction: Why Study More Trigonometry and Analytical Geometry?; How to Use It to Solve Complex Problems; Special Methods for Finding Area of a Triangle; Radius of a Circle; Law of Tangents; Half-Angle Formulas; Mollweide’s Equations; How to Use What You Have Learned; How a Man Named Hook Used Trigonometry and Analytical Geometry to Win a Job Promotion
Study Unit 5: Plane Trigonometry and Analytical Geometry, Part 5
Objectives of the Course; Variation of Trigonometric Functions; How to Graph Trigonometric Functions; Short Table of Natural Functions; Plotting and Sketching Sine and Cosine Curves; Table of Values; Other Features of Sine and Cosine Curves; Secant and Cosecant Curves; Trigonometric Equations
Study Unit 6: Analytical Geometry, Part 1
Introduction; Rectangular Coordinate System; Number Line; Labeling the Line; Distance on the Line; Points in a Plane; Locating Points with Negative Coordinates; The Four Quadrants; Equation of a Straight Line; Points Shown Graphically; Graph of a Linear Equation; Lines Parallel to Axes; Slope, Intercept, and Inclination Angle
Study Unit 7: Analytical Geometry, Part 2
Methods; Conic Sections; Circle Defined as a Locus; General Equation of a Circle; Translation of Axes; Ellipse Defined as a Locus; Problems Involving an Ellipse; Parabola and How to Sketch It; Hyperbola; Tangents of Conic Sections; Meaning of Function; Trigonometric Functions; Curves; Polar and 3-D Coordinate Systems
How it Works After registering for the Trigonometry and Analytical Geometry Course, all of your learning materials will be shipped directly to you. If you like, you can also go to our website and download some of your study materials to get a head start. Your learning materials will guide you through the course content, explaining concepts and operations through a series of lessons. After each lesson, you’ll take an exam which you can submit by phone or our website. As you pass each lesson, you’ll proceed to the next topic until you complete the course.
There are seven exams that need to be passed to complete your course in Trigonometry and Analytical Geometryand you’ll have up to 15 weeks to complete the course.
Support
If you should ever need help with your studies, you can e-mail or call our instructors who will gladly help you with any questions that you might have.
Study Time
Since there is no set class schedule, you study when and where it’s convenient for you. You can complete your course as quickly as you’d like.
Completion
When you have successfully completed your course, you will receive a letter of completion along with an official transcript listing your completed course(s) and grades. You can apply your course towards our Diploma Program or a diploma from your local High School (be sure to check with your school authorities regarding mandatory attendance policies and whether they agree that the Penn Foster High School Program is acceptable toward the completion of your high school education).
Accreditation
Penn Foster High School is accredited by The Middle States Commission on Secondary Schools; has met the high standards of integrity and performance set by the Accrediting Commission of the Distance Education and Training Council (DETC), Washington D.C., and is licensed by the Pennsylvania State Board of Private Licensed Schools.
Whether you’re looking for accelerated studies or credit recovery, regionally and nationally accredited Penn Foster High School provides the courses you need to complete your High School Diploma.
