What is the general solution for 8sin(2x)+1=6 ?

The general solution for 8sin(2x)+1=6 is x=(0.67513…)/2+pin,x= pi/2-(0.67513…)/2+pin

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8sin(2x)+1=6

8 sin (2 x) + 1 = 6

x = \frac{0.67513 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.67513 \dots}{2} + πn

Degrees

x = 19.34109 \dots^{\circ} + 18 0^{\circ} n, x = 70.65890 \dots^{\circ} + 18 0^{\circ} n

Solution steps

8 sin (2 x) + 1 = 6

Move

1

to the right side

8 sin (2 x) + 1 = 6

Subtract

1

from both sides

8 sin (2 x) + 1 - 1 = 6 - 1

Simplify

8 sin (2 x) = 5

8 sin (2 x) = 5

Divide both sides by

8

8 sin (2 x) = 5

Divide both sides by

8

\frac{8 sin ( 2 x )}{8} = \frac{5}{8}

Simplify

sin (2 x) = \frac{5}{8}

sin (2 x) = \frac{5}{8}

Apply trig inverse properties

sin (2 x) = \frac{5}{8}

General solutions for

sin (2 x) = \frac{5}{8}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 x = arcsin (\frac{5}{8}) + 2 πn, 2 x = π - arcsin (\frac{5}{8}) + 2 πn

2 x = arcsin (\frac{5}{8}) + 2 πn, 2 x = π - arcsin (\frac{5}{8}) + 2 πn

Solve

2 x = arcsin (\frac{5}{8}) + 2 πn : x = \frac{arcsin ( \frac{5}{8} )}{2} + πn

2 x = arcsin (\frac{5}{8}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{5}{8}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{5}{8} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( \frac{5}{8} )}{2} + πn

x = \frac{arcsin ( \frac{5}{8} )}{2} + πn

Solve

2 x = π - arcsin (\frac{5}{8}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{5}{8} )}{2} + πn

2 x = π - arcsin (\frac{5}{8}) + 2 πn

Divide both sides by

2

2 x = π - arcsin (\frac{5}{8}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{5}{8} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} - \frac{arcsin ( \frac{5}{8} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{5}{8} )}{2} + πn

x = \frac{arcsin ( \frac{5}{8} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{5}{8} )}{2} + πn

Show solutions in decimal form

x = \frac{0.67513 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.67513 \dots}{2} + πn

\frac{( 1 - cos ( x ) ) ( csc ^{2} ( x ) - 4 )}{1 + cos ( x )} = 0

6 sin (a) + 4 = 2 sin (a) + 8

sin (3 x) = 0, - 2 < x < 2

tan (x) = \frac{2}{6}

2 sin^{2} (x) - 5 sin (x) = 3

What is the general solution for 8sin(2x)+1=6 ?
The general solution for 8sin(2x)+1=6 is x=(0.67513…)/2+pin,x= pi/2-(0.67513…)/2+pin