Trigonometric equation

A trigonometric equation is any equation that contains a trigonometric function. In order to solve a trig equation, we have to use both the reference angle we have memorized and a lot of algebra we have learned. For example, solve sin(x)+2=3 for 0 degree < x< 360 degree. I'll first isolate the variable containing term. Sin(x)+2=3 sin(x)=1. Now I'll use the reference angle I have memorized x=90.

Verifying identities

We have different identities to deal with the trig formulas, and those identities makes it easier to solve. For example, sin^2x+cos^2x=1, and 1+tan^2x=sec^2x. In order to solve the problem completely, we should use some rules, first simplify more complicated side. Second, we should find their common denominators if it is possible. We should always change all trig function in terms of sine and cosine. And finally, we can try to plug them into the identities we learned this week. 

Tangent functions and graph

We learned how to solve and graph tangent equation. The tangent will be undefined wherever it's denominator is zero. The tangent wil be zero wherever it's numerator is zero. Therefore, the tangent will have vertical asymptotes wherever the cosine is zero. One basic knowledge about tangent is that it equals to sin/cosine. 

Chapter 3 review

We basically learned how to deal with polynomial function, long division, synthetic division, rational zero test, finding approximating zeros, and rational functions. For polynomial function, we learned that the a i are real numbers and are called coefficients, also the term an is assumed to be nonzero and is called the leading term. Then we learned how to use long division and synthetic division and we can use both way to divide functions. For approximating zeros, we divide the interval in half to find its midpoint and complete f(m).