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

Solution steps

8 sin (2 x) + 1 = 6

Move

1

to the right side

8 sin (2 x) = 5

Divide both sides by

8

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

Apply trig inverse properties

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

Solve

2 x = π - 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