What is the general solution for 1=4sin(x) ?

The general solution for 1=4sin(x) is x=0.25268…+2pin,x=pi-0.25268…+2pin

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1=4sin(x)

1 = 4 sin (x)

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

Degrees

x = 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 165.52248 \dots^{\circ} + 36 0^{\circ} n

Solution steps

1 = 4 sin (x)

Switch sides

4 sin (x) = 1

Divide both sides by

4

4 sin (x) = 1

Divide both sides by

4

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Show solutions in decimal form

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

tan (x) = \frac{45}{67}

k, 1.5 = 6 (- cos (\frac{k}{2}) + 1)

cos (t) = sin (2 t)

2 cos^{2} (x) = 1 - cos^{2} (x)

4 + 2 cos (2 x) = 6 cos (x)

What is the general solution for 1=4sin(x) ?
The general solution for 1=4sin(x) is x=0.25268…+2pin,x=pi-0.25268…+2pin