What is the general solution for sin(4x)= 3/4 ?

The general solution for sin(4x)= 3/4 is x=(0.84806…)/4+(pin)/2 ,x= pi/4-(0.84806…)/4+(pin)/2

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sin(4x)= 3/4

sin (4 x) = \frac{3}{4}

x = \frac{0.84806 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.84806 \dots}{4} + \frac{πn}{2}

Degrees

x = 12.14759 \dots^{\circ} + 9 0^{\circ} n, x = 32.85240 \dots^{\circ} + 9 0^{\circ} n

Solution steps

sin (4 x) = \frac{3}{4}

Apply trig inverse properties

sin (4 x) = \frac{3}{4}

General solutions for

sin (4 x) = \frac{3}{4}

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

4 x = arcsin (\frac{3}{4}) + 2 πn, 4 x = π - arcsin (\frac{3}{4}) + 2 πn

4 x = arcsin (\frac{3}{4}) + 2 πn, 4 x = π - arcsin (\frac{3}{4}) + 2 πn

Solve

4 x = arcsin (\frac{3}{4}) + 2 πn : x = \frac{arcsin ( \frac{3}{4} )}{4} + \frac{πn}{2}

4 x = arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

4

4 x = arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{arcsin ( \frac{3}{4} )}{4} + \frac{2 πn}{4}

Simplify

x = \frac{arcsin ( \frac{3}{4} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{3}{4} )}{4} + \frac{πn}{2}

Solve

4 x = π - arcsin (\frac{3}{4}) + 2 πn : x = \frac{π}{4} - \frac{arcsin ( \frac{3}{4} )}{4} + \frac{πn}{2}

4 x = π - arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

4

4 x = π - arcsin (\frac{3}{4}) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{π}{4} - \frac{arcsin ( \frac{3}{4} )}{4} + \frac{2 πn}{4}

Simplify

x = \frac{π}{4} - \frac{arcsin ( \frac{3}{4} )}{4} + \frac{πn}{2}

x = \frac{π}{4} - \frac{arcsin ( \frac{3}{4} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{3}{4} )}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{arcsin ( \frac{3}{4} )}{4} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.84806 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.84806 \dots}{4} + \frac{πn}{2}

23 sec (x) + 4 = 0

\frac{sin ( θ )}{60} = \frac{sin ( 4 5 ^{\circ} )}{246.26}

6 cos (θ) = 32

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

376 = 80 \cdot 24.7 \cdot cos (x)

What is the general solution for sin(4x)= 3/4 ?
The general solution for sin(4x)= 3/4 is x=(0.84806…)/4+(pin)/2 ,x= pi/4-(0.84806…)/4+(pin)/2