16.1. Fundamental Identities
In this section we will give the identities that we will use throughout this chapter. We will start with some we already know and go on to derive some new ones.
16.1.1. Reciprocal Relations
We have already encountered the reciprocal relations earlier, and we repeat them here.
In our next set of examples, we will show how to simplify a trigonometric expression, that is, to rewrite it as an equivalent expression with fewer terms, and eliminating fractions where possible. A good way to simplify many expressions is to change all their functions to only sines and cosines.
Example 1:Rewrite the expression
to one containing only sines and cosines, and simplify. Recall that sec2 θ is another way of writing (sec θ)2. Solution: Using Eq. 117b gives us
|
Screen for the exploration.
16.1.2. Quotient Relations
▪ Exploration:
Try this. In the same viewing window, graph
and
- y2 = tan x
using a heavier line for y2. What do you see? Can you propose a trigonometric identity ...
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