What is the general solution for sin(x/3)=-0.85 ?

The general solution for sin(x/3)=-0.85 is x=-3*1.01598…+6pin,x=3pi+3*1.01598…+6pin

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sin(x/3)=-0.85

sin (\frac{x}{3}) = - 0.85

x = - 3 \cdot 1.01598 \dots + 6 πn, x = 3 π + 3 \cdot 1.01598 \dots + 6 πn

Solution steps

sin (\frac{x}{3}) = - 0.85

Apply trig inverse properties

\frac{x}{3} = arcsin (- 0.85) + 2 πn, \frac{x}{3} = π + arcsin (0.85) + 2 πn

Solve

\frac{x}{3} = arcsin (- 0.85) + 2 πn : x = - 3 arcsin (\frac{17}{20}) + 6 πn

Solve

\frac{x}{3} = π + arcsin (0.85) + 2 πn : x = 3 π + 3 arcsin (0.85) + 6 πn

x = - 3 arcsin (\frac{17}{20}) + 6 πn, x = 3 π + 3 arcsin (0.85) + 6 πn

Show solutions in decimal form

x = - 3 \cdot 1.01598 \dots + 6 πn, x = 3 π + 3 \cdot 1.01598 \dots + 6 πn

2 cos (3 θ) = 2

tan (θ) = 2, 0 < θ < (\frac{π}{2}), sin (\frac{θ}{2})

sinh (a) = \frac{1}{2}

sin (x) = \frac{- 1}{\frac{5}{2}}

2 csc^{2} (θ) - 3 cot (θ) + 3 = 0

What is the general solution for sin(x/3)=-0.85 ?
The general solution for sin(x/3)=-0.85 is x=-3*1.01598…+6pin,x=3pi+3*1.01598…+6pin