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

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

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Popular >

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

Solution

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

Solution

x = - 2 \cdot 0.33983 \dots

Degrees

x = - 38.94244 \dots^{\circ}

Solution steps

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

Divide both sides by

- 3

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

Divide both sides by

- 3

\frac{- 3 sin ( \frac{x}{2} )}{- 3} = \frac{1}{- 3}

Simplify

sin (\frac{x}{2}) = - \frac{1}{3}

sin (\frac{x}{2}) = - \frac{1}{3}

Apply trig inverse properties

sin (\frac{x}{2}) = - \frac{1}{3}

General solutions for

sin (\frac{x}{2}) = - \frac{1}{3}

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

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

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

Solve

\frac{x}{2} = arcsin (- \frac{1}{3}) + 2 πn : x = - 2 arcsin (\frac{1}{3}) + 4 πn

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

Simplify

arcsin (- \frac{1}{3}) + 2 πn : - arcsin (\frac{1}{3}) + 2 πn

arcsin (- \frac{1}{3}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{3}) = - arcsin (\frac{1}{3})

= - arcsin (\frac{1}{3}) + 2 πn

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

- 2 arcsin (\frac{1}{3}) + 2 \cdot 2 πn : - 2 arcsin (\frac{1}{3}) + 4 πn

- 2 arcsin (\frac{1}{3}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= - 2 arcsin (\frac{1}{3}) + 4 πn

x = - 2 arcsin (\frac{1}{3}) + 4 πn

x = - 2 arcsin (\frac{1}{3}) + 4 πn

x = - 2 arcsin (\frac{1}{3}) + 4 πn

Solve

\frac{x}{2} = π + arcsin (\frac{1}{3}) + 2 πn : x = 2 π + 2 arcsin (\frac{1}{3}) + 4 πn

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

Multiply both sides by

2

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

Multiply both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 π + 2 arcsin (\frac{1}{3}) + 2 \cdot 2 πn : 2 π + 2 arcsin (\frac{1}{3}) + 4 πn

2 π + 2 arcsin (\frac{1}{3}) + 2 \cdot 2 πn

Multiply the numbers:

2 \cdot 2 = 4

= 2 π + 2 arcsin (\frac{1}{3}) + 4 πn

x = 2 π + 2 arcsin (\frac{1}{3}) + 4 πn

x = 2 π + 2 arcsin (\frac{1}{3}) + 4 πn

x = 2 π + 2 arcsin (\frac{1}{3}) + 4 πn

x = - 2 arcsin (\frac{1}{3}) + 4 πn, x = 2 π + 2 arcsin (\frac{1}{3}) + 4 πn

Solutions for the range

- \frac{π}{2} \leq x \leq \frac{π}{2}

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

Show solutions in decimal form

x = - 2 \cdot 0.33983 \dots

Graph

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Frequently Asked Questions (FAQ)

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