Trigonometric equations involve trigonometric functions and are solved by finding the angles that satisfy the given condition.
The simplest form of trigonometric equations is linear, such as:
$2 \sin x = 1, 0 \leq x \leq 2\pi$
To solve this:
For the equation $2 \sin 2x = 3 \cos x, 0° \leq x \leq 180°$:
Therefore, the solutions are approximately 48.6° and 90°.
Don't forget to pay attention to the possible domain of $x$. For example, consider the following equation:
$\sin(2x) = \frac{1}{2}, 0 \leq x \leq 2\pi$
If $0 \leq x \leq 2\pi$, that means $0 \leq 2x \leq 4\pi$! So the possible values of $2x$ are $\frac\pi6$, $\frac{5\pi}6$, $\frac{13\pi}6$, and $\frac{17\pi}6$, leading to:
$x = \frac{\pi}{12}$ or $x = \frac{5\pi}{12}$ or $x = \frac{13\pi}{12}$ or $x = \frac{17\pi}{12}$
If you see that $0 \leq x \leq \pi$ and assume that also applies to $2x$, you'll only get two of the solutions, and lose the final answer mark.
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