C2 - Formulae to learn

Question	Answer
sine rule	\(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\)
cosine rule	\(a^2 = b^2 + c^2 - 2 b c \cos A\)
area of triangle	Area \(= \frac{1}{2} b c \sin A\)
remainder when polynomial \(f(x)\) divided by \((x-a)\)	\(f(a)\)
\(a^b=c\)	\(b=\log_ac\)
\(\log_ax+\log_ay\)	\(\log_a(xy)\)
\(\log_ax-\log_ay\)	\(\log_a\big(\frac{x}{y}\big)\)
\(k\log_ax\)	\(\log_a(x^k)\)
\(\tan\theta\)	\(\frac{\sin\theta}{\cos\theta}\)
\(\cos^2\theta+\sin^2\theta\)	1
\(\pi\) radians	\(180^\circ\)
area of sector	A \( =\frac{1}{2}r^2\theta\)
\(\int x^n dx\) (\(n \neq -1\))	\(\frac{1}{n+1}x^{n+1}+c\)
\(\int \Big( f'(x) + g'(x) \Big) dx\)	\(f(x) + g(x) + c\)
area between curve, x-axis and points \(a\) \(b\)	\(\int\limits_a^b y dx \) (when \(y \ge 0\))
area between curve, y-axis and points \(c\) \(d\)	\(\int\limits_c^d x dy \) (when \(x \ge 0\))

Resource summary

	Created by Tech Wilkinson about 10 years ago