FTCE Math Study Questions with Verified Answers

Sin90° or π/2 - 1 Cos90° or π/2 - 0 Tan90° or π/2 - Infinity Cot90° or π/2 - 0 Sin^2+cos^2 - 1 1+tan^2 - sec^2 1+cot^2 - csc^2 Arcsin - sin^-1 or the inverse of sin Process of induction - the process of making inferences based upon specific, concrete cases or examples. S^2 or variance - (Σ(x-x̅)^2)/(n-1) Standard Deviation (s) - √(Σ(x-x̅)^2)/(n-1) Simple linear Regression - y=a+bxi b=(Σxy-nx̅ȳ)/(Σx^2 - nx̅^2) a=(Σy - bσy)/n Sin(x+h) - sin(x)cos(h) + cos(x)sin(h) Lim [cos(x) - 1]/x as x -- 0 - = 0 Lim sin(x)/x as x -- 0 - = 1 Area of equilateral triangle - or .433(s^2) Product Rule in Derivatives h(x) = f(x)g(x) - h'(x) = f'(x)g(x) + f(x)g'(x) Quotient Rule of Derivatives h(x) = f(x)/g(x) - h'(x) = [f'(x)g(x) - f(x)g'(x)]/ g(x)^2 Implicit differentiation - substitute the extra variables as a function of the variable you're trying to derive. Ex: if you are deriving a function in respect to x and there is a y variable substitute y for y(x). Derivative of ln(x) - = 1/x Explained: Ln(x)=y X=e^y 1/(e^y) = dy/dx 1/x = dy/dx 1/x = d[ln(x)]/dx