What is the general solution for sin(x)=-1/3 ,0<= x<= 2pi ?

The general solution for sin(x)=-1/3 ,0<= x<= 2pi is x=pi+0.33983…,x=-0.33983…+2pi

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sin(x)=-1/3 ,0<= x<= 2pi

sin (x) = - \frac{1}{3}, 0 \leq x \leq 2 π

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

Degrees

x = 199.47122 \dots^{\circ}, x = 340.52877 \dots^{\circ}

Solution steps

sin (x) = - \frac{1}{3}, 0 \leq x \leq 2 π

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

Solutions for the range

0 \leq x \leq 2 π

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

Show solutions in decimal form

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

What is the general solution for sin(x)=-1/3 ,0<= x<= 2pi ?
The general solution for sin(x)=-1/3 ,0<= x<= 2pi is x=pi+0.33983…,x=-0.33983…+2pi