What is the general solution for 4sin(x)=2.54648 ?

The general solution for 4sin(x)=2.54648 is x=0.69010…+2pin,x=pi-0.69010…+2pin

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4sin(x)=2.54648

4 sin (x) = 2.54648

x = 0.69010 \dots + 2 πn, x = π - 0.69010 \dots + 2 πn

Degrees

x = 39.54024 \dots^{\circ} + 36 0^{\circ} n, x = 140.45975 \dots^{\circ} + 36 0^{\circ} n

Solution steps

4 sin (x) = 2.54648

Divide both sides by

4

4 sin (x) = 2.54648

Divide both sides by

4

\frac{4 sin ( x )}{4} = \frac{2.54648}{4}

Simplify

sin (x) = \frac{2.54648}{4}

sin (x) = \frac{2.54648}{4}

Apply trig inverse properties

sin (x) = \frac{2.54648}{4}

General solutions for

sin (x) = \frac{2.54648}{4}

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

x = arcsin (\frac{2.54648}{4}) + 2 πn, x = π - arcsin (\frac{2.54648}{4}) + 2 πn

x = arcsin (\frac{2.54648}{4}) + 2 πn, x = π - arcsin (\frac{2.54648}{4}) + 2 πn

Show solutions in decimal form

x = 0.69010 \dots + 2 πn, x = π - 0.69010 \dots + 2 πn

y, \frac{3}{2} = sin (arcsin (0) + y)

2 \cdot cos^{2} (x) - cos (x) - 1 = 0

tan^{2} (x) - cot (x) = 0

5 sec^{3} (x) - 20 sec (x) = 0

3 cot^{2} (x) - 1 = 0, x

What is the general solution for 4sin(x)=2.54648 ?
The general solution for 4sin(x)=2.54648 is x=0.69010…+2pin,x=pi-0.69010…+2pin