Trig+Equations+&+Laws;+Vectors

=**Unit 7: Trigonometry Extended & Applied (including Vectors)**=



=Helpful Videos: Kelsey Parkhill=

=media type="custom" key="25779872" width="80" height="80"= This short video is great for beginners in trying to understand how to solve trigonometric equations. He worked a simple problem all the way through, showing how to solve for multiple answers.

media type="custom" key="25779832" width="50" height="50" This video was extremely thorough in explaining how to use the Law of Sines to solve a complete triangle, showing multiple scenarios and ways to work out the problems.

media type="custom" key="25894650" width="100" height="100" A great video for people new to working with vectors. He teaches a variety of way to look at vectors to gain a better understanding of them, using several analogies and perspectives. He also shows you how to add vectors, looking at a problem from both an algebraic and a graphic view.

media type="custom" key="25894694" Another helpful video for learning about vectors. This one shows how to solve for the magnitude of a vector.

=Helpful Sites: (Hollie Bryan)=

[] This objective of this website is to help distinguish whether law of sine or law of cosine should be used when trying to find the angles or side lengths of a triangle. it gives a basic explanation of how you know when to use which law along with giving examples of each. Also, this website is good for those who want to have step-by-step examples at hand.

[] This website provides an in-depth explanation of both law of sine and law of cosine. It breaks each section down where it can be easily understood, and with doing so, also gives the equation(s) and some example triangles to go along with each. It does not give any specific examples, but works just with variables in many different cases to help us understand how one part of the equation might equal the second part.

[] This website focuses mainly of the law of cosine. It gives the equation for it, and immediately afterwards, goes through a step-by-step example to give us an understanding of how the equation works. It gives ways to remember the equation and explains the times in which you should use the law of cosine to figure out all the information of a triangle. Done with the examples? Ten additional Try-It-Yourself problems can be found at the bottom.

[] The website focuses on solving trigonometric equations. Even though it focuses on degrees rather than the unit circle as a whole, it shows how to isolate terms and work through and equations. It walks through a variety of problems, almost any that might be encountered, including those with no solution, some that consist of factoring, and ones where trig-identities are needed.

[] This website has more of a jump-right-in approach. Instead of really explaining anything about trig equations and how to solve them, it goes straight into an example so you can actually see it. The website includes a total of five examples that are very detailed, allowing us to see every little step and know exactly what's going on. As it goes through each problem, it gives all the possible answers and works out each possibility. Through the use of numbers, specifics, and the unit circle, we can have leave with a good understanding of exactly how to solve trig equations.

[] This website has all the basics when it comes to vectors. Easy to follow along with, it starts with the definition and works its way from there including all aspects of the topic: addition, subtraction, magnitude, scalar, and multiplication. This site is filled with step-by-step examples of each sub-topic, along with ten available try-it-yourself problems at the bottom for review.

[] This website breaks apart each topic into its own section to help us better understand them. It starts off with a simple outline of how each sub-topic comes together in "vector operations", and from there, starts at the beginning to give us interaction problems so we can try as we go, without having the issue of being confused.

=Possible Careers Using Trigonometry (Nicholas McConnell)=
 * **Architect-** they work closely with shapes and structures and must rely on trigonometry to express and design shapes and structures that don't exist yet.
 * [[image:http://2.bp.blogspot.com/-868OTsjlAik/TkFPMVn_9nI/AAAAAAAACZY/zxLzNnxQ6K4/s320/trig__6bafcd9e.jpg]]
 * **Carpenter**- they use trig when they cut wood so they know what measurements to use, as well as when they make a floor plan so they know what they need ahead of time.
 * [[image:http://www.wkfinetools.com/mlibrary/Griffith-Ira/1916-Carpentry/0_img-pdf/1.jpg]]media type="custom" key="25835658"

ex: x^2+4x+4 (x+2)(x+2) Cos^2x=1-Sin^2x Sin^2x=1-Cos^2x Sec^2x=1+tan^2x Tan^2x=Sec^2x-1 Cot^2x=Csc^2x-1 Csc^2x=Cot^2x+1 Csc=1/Sin Sec=1/Cos Cot=1/Tan or Cos/Sin
 * Prerequisite Skills (Jason Chow-Sam)**
 * Rounding: 4 and below let it go,5 and above give it a shove.
 * Factoring: The equation is factored into 2 seperate equations, that when multiplied by each other make the equation. The intergers in the 2 factored equations multilpy to equal the non-variable interger in the non-factored equation, the intergers in the 2 factored equations add to equal the numeric coefficient of the non-exponential variable in the original equation, and that the variables in the 2 factored equations multiply to the exponential variable in the original equation.
 * Knowing the Unit Circle
 * Pythagorean Identities:
 * Knowing reciprocal forms/functions of base functions: SIn, Cos, Tan

** Mathematics 1001: Absolutely Everything That Matters About Mathematics in 1001 Bite-Sized Explanations ** By Dr. Richard Elwes

**Annotated Bibliography ** Jenna Labbie