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

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

x = - 2 \cdot 0.33983 \dots

Solution steps

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

Divide both sides by

- 3

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

Apply trig inverse properties

\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

Solve

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

2 sin^{2} (θ) - 5 sin (θ) - 3 = 0

4 cos^{2} (x) - 4 cos (x) - 1 = 0, 0 \leq x \leq 2 π

10 = 6.7 + 13.75 tan (θ) - 4.718 (1 + tan^{2} (θ))

2 cos (3 θ) = - 3

cos (θ) = - cos (θ)

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…