What is the general solution for 3sin(x)=1 ?

The general solution for 3sin(x)=1 is x=0.33983…+2pin,x=pi-0.33983…+2pin

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3sin(x)=1

3 sin (x) = 1

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

Degrees

x = 19.47122 \dots^{\circ} + 36 0^{\circ} n, x = 160.52877 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 sin (x) = 1

Divide both sides by

3

3 sin (x) = 1

Divide both sides by

3

\frac{3 sin ( x )}{3} = \frac{1}{3}

Simplify

sin (x) = \frac{1}{3}

sin (x) = \frac{1}{3}

Apply trig inverse properties

sin (x) = \frac{1}{3}

General solutions for

sin (x) = \frac{1}{3}

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

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

4 sec (x) csc (x) = 8 csc (x)

sec (x) - 1 = tan (x)

cos (x) + 3 sin (x) = 1

tan (t) = 1

sin (x) = \frac{9}{41}

What is the general solution for 3sin(x)=1 ?
The general solution for 3sin(x)=1 is x=0.33983…+2pin,x=pi-0.33983…+2pin