What is the general solution for 6sin(4x)+4=5 ?

The general solution for 6sin(4x)+4=5 is x=(0.16744…)/4+(pin)/2 ,x= pi/4-(0.16744…)/4+(pin)/2

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6sin(4x)+4=5

6 sin (4 x) + 4 = 5

x = \frac{0.16744 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.16744 \dots}{4} + \frac{πn}{2}

Degrees

x = 2.39851 \dots^{\circ} + 9 0^{\circ} n, x = 42.60148 \dots^{\circ} + 9 0^{\circ} n

Solution steps

6 sin (4 x) + 4 = 5

Move

4

to the right side

6 sin (4 x) + 4 = 5

Subtract

4

from both sides

6 sin (4 x) + 4 - 4 = 5 - 4

Simplify

6 sin (4 x) = 1

6 sin (4 x) = 1

Divide both sides by

6

6 sin (4 x) = 1

Divide both sides by

6

\frac{6 sin ( 4 x )}{6} = \frac{1}{6}

Simplify

sin (4 x) = \frac{1}{6}

sin (4 x) = \frac{1}{6}

Apply trig inverse properties

sin (4 x) = \frac{1}{6}

General solutions for

sin (4 x) = \frac{1}{6}

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

4 x = arcsin (\frac{1}{6}) + 2 πn, 4 x = π - arcsin (\frac{1}{6}) + 2 πn

4 x = arcsin (\frac{1}{6}) + 2 πn, 4 x = π - arcsin (\frac{1}{6}) + 2 πn

Solve

4 x = arcsin (\frac{1}{6}) + 2 πn : x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

4 x = arcsin (\frac{1}{6}) + 2 πn

Divide both sides by

4

4 x = arcsin (\frac{1}{6}) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{2 πn}{4}

Simplify

x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

Solve

4 x = π - arcsin (\frac{1}{6}) + 2 πn : x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

4 x = π - arcsin (\frac{1}{6}) + 2 πn

Divide both sides by

4

4 x = π - arcsin (\frac{1}{6}) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{2 πn}{4}

Simplify

x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.16744 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.16744 \dots}{4} + \frac{πn}{2}

29 cos (x) = - 17 - cos (x)

2 cos (x) + 2 cos (2 x) = 0

cos^{2} (x) + sin (x) = 0

tan (x) = \frac{- 3}{3}

tan (\frac{x}{3}) = \frac{3}{3}

What is the general solution for 6sin(4x)+4=5 ?
The general solution for 6sin(4x)+4=5 is x=(0.16744…)/4+(pin)/2 ,x= pi/4-(0.16744…)/4+(pin)/2