Simplify+Trigonometric+Expressions

Kyle Gain =__**Simplifying trigonometric expressions**__= __**Reflection:**__ Overall, I enjoyed this particular section. It is interesting to me because it is somewhat like a puzzle that you need to solve, and thinking about it like this makes it more enjoyable for me. At first, it was somewhat difficult for me to understand what to do to solve the problems, but as I worked through enough examples, I gradually got a better feel for how to approach the different problems. It also helped when I started to memorize the different trig identities, since it helped me to understand how the problems worked and what would work better in order to solve them.


 * __Explanation:__** Simplifying trigonometric expressions is using the basic trig identities and any other simplifying rules to help put a trig expression in its simplest terms. There can be several ways to go about any of these problems, but there is usually one way that is easier than the others. Generally, it is easiest to try to put everything in terms of cosine and sine, as many of the trig identities involve these two. It is also important to look for areas where trig identities can be used and substituted into the expression to help with simplifying. Finally, try to factor the expressions to make them easier to work with for some of the more complicated expressions. Here are some example problems:

__**Examples**__: Explanation: Simplify: tanxcscx/secx 1) Change tanx to sinx/cosx using the quotient identity, and change cscx to 1/sinx using the reciprocal identity. 2) Cancel out the sinx/sinx. 3) Change secx to 1/cosx using the reciprocal identity. 4) Cancel out cosx/cosx. 5) You are left with 1, therefore it is simplified. Work:
 * (Easy)**

Explanation: Simplify: 1/sin^2x - cos^2x/sin^2x 1) Since the two fractions have a common denominator, subtract the two fractions giving you 1-cos^2x/sin^2x. 2) Using the pythagorean identity, change 1-cos^2x to sin^2x. 3) Since you are left with sin^2x/sin^2x, simply divide the two and you are left with 1. Work: Explanation: Simplify: cos^4x+2cos^2xsin^2x+sin^4x 1) First, factor the expression to get (cos^2x+sin^2x)(cos^2x+sin^2x). 2) Use the pythagorean identity to make both expressions equal to 1. 3) Multiply 1*1 to get 1. Work: __**Class Problem:**__
 * (Medium)**
 * (Hard)**

media type="file" key="trig project video.mp4"
 * __Video:__**