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.
Easy ways to remember trigonometric identities
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calculus
trigonometry
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7http://en.wikipedia.org/wiki/Euler's_formula – 2012-10-17
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1There 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
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0In 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