Expert: Sherry Wallin - 6/11/2011

Question
I am getting ready to go to the 11th grade this coming school year and am taking AP English, Chemistry, Trigonometry,and Algebra 3.The only reason why I mentioned these is because they will be my hardest,even though I am a straight A student.I was wondering what can I do to prepare for these classes?What should I know for these subjects?Are they hard?Can someone give me a list of things I should know?

Answer
Hi Corrina~

I can help you with what you will need to know for Trigonometry and Algebra 3, but you will need to tell me what you covered in Algebra 2 because most high schools have just algebra 1 and algebra 2. Maybe your school breaks the curriculum of Alg 1 and Alg 2 into 3 parts.
For trigonometry you will want to know Pythagorean's Theorem (a^2 + b^2 = c^2 where a and b are the legs of a right triangle and c is the hypotenuse of the right triangle) forwards and backwards. You will need to know the 6 trigonometric functions:
sine * (sin *), cosine * (cos *), tangent * (tan *), cotangent * (cot *), secant * (sec *), and cosecant * (cscc *), where I have used '*' to mean angle and the stuff in the parentheses is shorthand for each function. It is important to note that you CANNOT talk about any of the functions without an argument and in this case the angle '*' is the argument. There is a cool way to understand what the 6 trig functions do and it is written 'sohcahtoa'. The s stands for sin *, o for opposite side, h for hypotenuse (of a right triangle), c for cos *, and t for tan *. The other 3 trig functions that I mentioned above are related to the 3 I just mentioned. Here are the relationships: sin * = 1/csc *; cos * = 1/sec *; tan * = 1/cot * and vice versa you have csc * = 1/sin *; sec * = 1/cos *; and cot * = 1/tan *. There are a few more important facts to know about how these 6 trig functions are related and these are: cos^2 * + sin ^2* = 1 and can also be written as (cos *)^2 + (sin *)^2 = 1 and sec^2* = 1 + tan^2* as well as csc^2* = cot^2* + 1
And finally another useful relationship is that the sin * and cos* are complements of each other. If I want the sin 30 deg It is the same as the cos 60 deg and the relationship is often written as sin(90-*) = cos * or cos(90-*) = sin *.

If you have any further questions please feel free to ask.

Math Prof