Trigonometry

Oblique Triangles in Applications

Having just looked at how to solve oblique triangles, let’s look at a couple “word problems” (applications) involving such triangles. We’ll be using the Law of Sines, and also exploring alternative methods of solution. A tilted tree Let’s start with this real application from 1999: Will the Tree Hit the House? There is a tree …

Oblique Triangles in Applications Read More »

Proving the Law of Cosines

Last week we looked at several proofs of the Law of Sines. Here we will see a couple proofs of the Law of Cosines; they are more or less equivalent, but take different perspectives – even one from before trigonometry and algebra were invented! Proof using coordinates First, here is a question we looked at …

Proving the Law of Cosines Read More »

Proving the Law of Sines

Two of the most useful facts in trigonometry are the Law of Sines and the Law of Cosines (sometimes called the Sine Rule or Sine Formula, and the Cosine Rule or Cosine Formula). Over the years we were often asked where they come from (or are just asked about them, and reflexively offer proofs). There …

Proving the Law of Sines Read More »

Order of Operations: Trigonometric Functions

(An archive question of the week) Last time we looked at some details that are rarely mentioned in stating the conventions for interpreting algebraic expressions. I couldn’t fit a discussion of the most complicated case: trigonometric functions, which when written without parentheses, as they traditionally have been, can raise several issues. (Much of the same …

Order of Operations: Trigonometric Functions Read More »

An Introduction to Trigonometry

(An archive question of the week) While I’m showing some recent explanations of basic trigonometry techniques, this is a good time to look at an even more basic explanation of the essentials of the subject for a beginner. Right triangle trigonometry Here is the question, from 2001: Trigonometry in a Nutshell I’m in 8th grade …

An Introduction to Trigonometry Read More »