Topic: The Six Trigonometric Functions
Subtopic: Angles
Overview
We start the course with some basic terminology and geometry primarily related to angles and triangles. Be sure to memorize the circle diagram which indicates all the "special angles" at 30°, 45°, 60°, 90°, etc.
Objectives
By the end of this topic you should know and be prepared to be tested on:
- 1.1.1 Solve problems using the "180° in a triangle" theorem
- 1.1.2 Solve problems using the Pythagorean theorem
- 1.1.3 Recognize and use the two "special" triangles (45°-45°-90° and 30°-60°-90°)
- 1.1.4 Recognize and use Pythagorean triples
- 1.1.5 Know the circle diagram and what it means for an angle to be in "standard position" on the circle diagram
- 1.1.6 Know the difference among positive angles, negative angles, and quadrantal angles
- 1.1.7 Find angles coterminal to a given angle
Terminology
Define: degree, right angle, straight angle, acute angle, obtuse angle, complimentary angles, supplementary angles, coterminal angles, quadrantal angles, right triangle, acute triangle, obtuse triangle, equilateral triangle, equiangular triangle, isosceles triangle, theorem
Supplementary Resources
Two readings by David Joyce of Clark University:
A History of Trigonometry and
What is Trigonometry?
Information on Pythagoras, the Pythagorean Theorem, and Pythagorean Triples:
Bio: Pythagoras of Samos
Proof of the Pythagorean Theorem
History of the Pythagorean Theorem
Pythagorean Triple Calculator