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

Degrees

x = - 174.63500 \dots^{\circ} + 108 0^{\circ} n, x = 714.63500 \dots^{\circ} + 108 0^{\circ} n

Solution steps

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

Apply trig inverse properties

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

General solutions for

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

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

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

\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

\frac{x}{3} = arcsin (- 0.85) + 2 πn

Simplify

arcsin (- 0.85) + 2 πn : - arcsin (\frac{17}{20}) + 2 πn

arcsin (- 0.85) + 2 πn

arcsin (- 0.85) = - arcsin (\frac{17}{20})

arcsin (- 0.85)

= arcsin (- \frac{17}{20})

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{17}{20}) = - arcsin (\frac{17}{20})

= - arcsin (\frac{17}{20})

= - arcsin (\frac{17}{20}) + 2 πn

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

Multiply both sides by

3

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

Multiply both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

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

- 3 arcsin (\frac{17}{20}) + 3 \cdot 2 πn

Multiply the numbers:

3 \cdot 2 = 6

= - 3 arcsin (\frac{17}{20}) + 6 πn

x = - 3 arcsin (\frac{17}{20}) + 6 πn

x = - 3 arcsin (\frac{17}{20}) + 6 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

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

Multiply both sides by

3

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

Multiply both sides by

3

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

Simplify

x = 3 π + 3 arcsin (0.85) + 6 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