Answer to Question #229496 in Algebra for Ann

Question

Which one of the following is the set of solutions of Sin(3x) + Cos(3x) =0 on the interval ( - pie + pie)?

1.(-5pie/ 12, -pie/12, pie/4, 7pie/12)

2.(-pie/4, -pie/12, pie/4, 7pie/12,11pie/12)

3.(-3pie/4, -5pie/12, - pie/12, pie/4, 7pie/12, 11pie/12)

4.None of the preceding.

Answer 1

$\displaystyle sin(3x) + cos(3x) = 0 \\sin(3x) = -cos(3x) \\tan(3x) = -1 \\\implies 3x = -\frac{\pi}{4}+k\pi, k \in \mathbb{Z} \\x= -\frac{\pi}{12}+\frac{k\pi}{3} \\\text{Since x $\in (-\pi, \pi), -2\leq k \leq 3$ } \\\text{Thus the solution set is }\{-\frac{3\pi}{4}, -\frac{5\pi}{12},-\frac{\pi}{12},\frac{\pi}{4}, \frac{7\pi}{12}, \frac{11\pi}{12} \}$