What is the general solution for -8*sin(0.784+x)=0 ?

The general solution for -8*sin(0.784+x)=0 is x=6.28318…n-0.784,x=pi+6.28318…n-0.784

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-8*sin(0.784+x)=0

- 8 \cdot sin (0.784 + x) = 0

x = 6.28318 \dots n - 0.784, x = π + 6.28318 \dots n - 0.784

Degrees

x = - 44.91989 \dots^{\circ} + 36 0^{\circ} n, x = 135.08010 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- 8 sin (0.784 + x) = 0

Divide both sides by

- 8

- 8 sin (0.784 + x) = 0

Divide both sides by

- 8

\frac{- 8 sin ( 0.784 + x )}{- 8} = \frac{0}{- 8}

Simplify

sin (0.784 + x) = 0

sin (0.784 + x) = 0

General solutions for

sin (0.784 + x) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

0.784 + x = 0 + 2 πn, 0.784 + x = π + 2 πn

0.784 + x = 0 + 2 πn, 0.784 + x = π + 2 πn

Solve

0.784 + x = 0 + 2 πn : x = 6.28318 \dots n - 0.784

0.784 + x = 0 + 2 πn

0 + 2 πn = 2 πn

0.784 + x = 2 πn

Move

0.784

to the right side

0.784 + x = 2 πn

Subtract

0.784

from both sides

0.784 + x - 0.784 = 2 πn - 0.784

Simplify

x = 6.28318 \dots n - 0.784

x = 6.28318 \dots n - 0.784

Solve

0.784 + x = π + 2 πn : x = π + 6.28318 \dots n - 0.784

0.784 + x = π + 2 πn

Move

0.784

to the right side

0.784 + x = π + 2 πn

Subtract

0.784

from both sides

0.784 + x - 0.784 = π + 2 πn - 0.784

Simplify

x = π + 6.28318 \dots n - 0.784

x = π + 6.28318 \dots n - 0.784

x = 6.28318 \dots n - 0.784, x = π + 6.28318 \dots n - 0.784

6 sin^{2} (x) + 5 sin (x) + 1 = 0

3 tan^{2} (x) + 3 tan (x) = 0

arcsin (x) = arcsin (\frac{2}{5}) + arcsin (\frac{3}{5})

3 tan^{2} (x) + tan (x) = 0

tan^{2} (x) - 4 sin (x) + 4 = 0

What is the general solution for -8*sin(0.784+x)=0 ?
The general solution for -8*sin(0.784+x)=0 is x=6.28318…n-0.784,x=pi+6.28318…n-0.784