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Polar Coordinates

Polar coordinates are essentially points points on a graph. They are not, however, plotted on a traditional x-y plane, but a circle. Also, the points are not listed as (x,y), but rather (r,ø). The R sands for radius, and the ø stands for angle. These points, however, can be converted to (x,y) terms by going through specific equations for each coordinate. 

2nd semester blog

Last semester I thought that I did well on taking notes, doing my homework, and preparing for tests. This semester, however, I would like to be more on top of my blogs, know when upcoming quizzes are, and study more even when there is no upcoming test or quiz. My favorite Christmas story was the first Monday of break me and by brother went hiking and I got poison oak all over my body and I had it for two weeks. Just kidding that was terrible, I enjoyed snowboarding almost every day though.

Law of sines and cosines

The law of sines is sin(A)/a=sin(B)/b. It is used when you have two angles and one side. The law of cosines is c^2=a^2+b^2-2abcos(C). This is used when you have three sides or two sides and an angle. Both of these are used to find the angles and sides of non-right triangles. Each law can be used in terms of a, b, or c.

Verifying trig identities

Essentially to verify a trig identity you must use different forms of substituting trig functions. One major one is tan=sin/cos. Another common one is sin^2+cos^2=1. 1+tan^2=sec^2 and 1+cot^2=csc^2 are also very commonly used. In many ways, verifying trig identities is like solving a puzzle. You must chose the most complicated side to work one, and use only that side. Most of the times you start by putting everything in terms of sin and cos.

Tangent

Tangent is a trigonometric function. Tangent can also be graphed. When trying to find an angle of a right right triangle, you would use tangent by saying tan(angle)=opposite/adjacent. The graph of tangent is not continuous. No matter what transformation the tangent graph goes through, there will always be infinite zeros. There are various trig identifies concerning tangent, including sum/difference, half angle, and double angle identities. Tangent is equal to sine over cosine. 

Sine and cosine

Sine and cosine are trigonometric functions. They both can be graphed. When trying to find an angle of a right right triangle, you would use sine by saying sin(angle)=opposite/hypotenuse. If you were to use cosine, you would say cos(angle)=adjacent/hypotenuse. Both sine and cosine's graphs are very similar, except that sine starts at x=0 while cosine starts at the high test point of the graph's period. There are various trig identifies concerning sine and cosine, including sum/difference, half angle, and double angle identities.