What is the general solution for 5sin(4x)=2 ?

The general solution for 5sin(4x)=2 is x=(0.41151…)/4+(pin)/2 ,x= pi/4-(0.41151…)/4+(pin)/2

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5sin(4x)=2

5 sin (4 x) = 2

x = \frac{0.41151 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.41151 \dots}{4} + \frac{πn}{2}

Solution steps

5 sin (4 x) = 2

Divide both sides by

5

sin (4 x) = \frac{2}{5}

Apply trig inverse properties

4 x = arcsin (\frac{2}{5}) + 2 πn, 4 x = π - arcsin (\frac{2}{5}) + 2 πn

Solve

4 x = arcsin (\frac{2}{5}) + 2 πn : x = \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}

Solve

4 x = π - arcsin (\frac{2}{5}) + 2 πn : x = \frac{π}{4} - \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{arcsin ( \frac{2}{5} )}{4} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.41151 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.41151 \dots}{4} + \frac{πn}{2}

2 cos^{2} (x) - 3 \cdot sin^{2} (x) - 2 = 0

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2 sin (x) = \frac{( 4 sin ( x ) - cos ( x ) )}{2}

cos (x + 60) \cdot cos (x - 60) = \frac{1}{2}

\frac{cos ( 2 x + 9 )}{3} = \frac{1}{2}

What is the general solution for 5sin(4x)=2 ?
The general solution for 5sin(4x)=2 is x=(0.41151…)/4+(pin)/2 ,x= pi/4-(0.41151…)/4+(pin)/2