Chapter 5 - Analytic Trigonometry"Although the title of this chapter suggests that we are now moving into the analytic phase of our study of trigonometric functions, the truth is that we have been in that phase for several sections already. Once the transition is made from triangle ratios to functions and their graphs, one is on analytic soil.
But our primary applications of trigonometry so far have been computational; we have not made full use of the properties of the functions to study the connections among the trigonometric functions themselves. In this chapter we will shift our emphasis more toward theory and proof, exploring where the properties of these special functions lead us, often with no immediate concern for real- world relevance at all. We hope in the process to give you an appreciation for the rich and intricate tapestry of interlocking patterns that can be woven from the six basic trigonometric functions—patterns that will take on even greater beauty later on when you can view them through the lens of calculus." (Demana, Franklin D. "Chapter 5." Precalculus: Graphical, Numerical, Algebraic. 7th ed. Boston: Addison-Wesley, 2007. 444. Print.) |
"It is no surprise that naturalists seeking to estimate wildlife populations must have an understanding of geometry (a word which literally means “earth measurement”). You will learn in this chapter that trigonometry, with its many connections to triangles and circles, enables us to extend the problem-solving tools of geometry significantly. On page 493 we will apply a result called Heron’s Formula (which we prove trigonometrically) to estimate the local density of a deer population."
(Demana, Franklin D. "Chapter 5." Precalculus: Graphical, Numerical, Algebraic. 7th ed. Boston: Addison-Wesley, 2007. 443. Print.) |
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Lesson 5.1 - Fundamental Identities
This lesson will cover identities, basic trig identities, pythagorean identities, cofunction identities, odd-even identities, simplifying trig identities and solving trig equations. |
Lesson 5.2 - Proving Trigonometric Identities
This lesson will cover proof strategies, proving identities, disproving non-identities, and identities in calculus. |
