How do you find the solutions to $8 {sin}^{2} (3 x) = - 7 sin (3 x)$ $8sin^2(3x) = -7sin(3x)$ ?

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How do you find the solutions to $8 {sin}^{2} (3 x) = - 7 sin (3 x)$ $8sin^2(3x) = -7sin(3x)$ ?

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Answer 1 · 2015-10-22T03:31:25

Solve 8sin^2 (3x) = - 7sin (3x)

Ans: $- 20^{\circ} 35 and 80^{\circ} 35$ $-20^@35 and 80^@35$

Explanation:

$8 {sin}^{2} (3 x) + 7 sin (3 x) = 0$ $8sin^2 (3x) + 7sin (3x) = 0$
Put sin (3x) in common factor:
$sin (3 x) (8 sin 3 x + 7) = 0$ $sin (3x)(8sin 3x + 7) = 0$

a. $sin 3 x = 0$ $sin 3x = 0$ --> 3x = 0 --> x = 0
$sin 3 x = π$ $sin 3x = pi$ --> $x = \frac{π}{3}$ $x = pi/3$
$sin 3 x = 2 π$ $sin 3x = 2pi$ --> $x = \frac{2 π}{3}$ $x = (2pi)/3$
b. 8sin (3x) + 7 = 0 --> $sin 3 x = - \frac{7}{8}$ $sin 3x = -7/8$
3x = - 61.04 --> x = $- 20^{\circ} 35$ $-20^@35$
3x = 180 - (-61.04) = 241.04 --> $x = 80^{\circ} 35$ $x = 80^@35$

Check by calculator
x = 80.35 3x = 241.04 --> sin 3x = -0.875 --> ${sin}^{2} (3 x) = 0.77$ $sin^2 (3x) = 0.77$
$8 {sin}^{2} (3 x) = 0.77 (8) = 6.12$ $8sin^2 (3x) = 0.77(8) = 6.12$ --> $- 7 sin 3 x = 7 (0.875) = 6.125$ $-7sin 3x = 7(0.875) = 6.125$ . OK

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How do you find the solutions to $8 {sin}^{2} (3 x) = - 7 sin (3 x)$ $8sin^2(3x) = -7sin(3x)$ ?

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Explanation:

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