2
$\begingroup$

Are there any easy ways or mnemonics to memorize the trigonometric identities like for example $$ \sin(3x) = 3\sin(x) - 4\sin^3(x) $$ I find them quite difficult to come up with, I almost always need to look them up.

  • 7
    http://en.wikipedia.org/wiki/Euler's_formula2012-10-17
  • 1
    There are some ad hoc tricks but these are highly identity dependent. For instance, $\sin(3x)$ in terms of $\sin(x)$ cannot have $\sin^2(x)$ term since $\sin(3x)$ is odd. Hence, $ \sin(3x) = a \sin(x) + b \sin^3(x)$. $x = \pi/2 \implies a+b = -1$ and $x = \pi/2 \implies a + b/2 = 1$. This gives us $b=-4$ and $a=3$. In general, $\sin((2n+1)x)$ is a polynomial $2n+1$ degree polynomial in $\sin(x)$ with only odd powers.2012-10-18
  • 0
    In addition to the other responses, it is fairly easy to derive them using the sum-difference trig formulas, so remembering those can be used to derive all other trig identities.2012-10-18

2 Answers 2