What is the general solution for sin(2x)=0.3,-180\circ <= x<= 180 ?

The general solution for sin(2x)=0.3,-180\circ <= x<= 180 is

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sin(2x)=0.3,-180\circ <= x<= 180

sin (2 x) = 0.3, - 180 \circ \leq x \leq 18 0^{\circ}

x = 0.15234 \dots, x = \frac{18 0 ^{\circ} - 0.30469 \dots}{2}, x = - 2.98924 \dots, x = \frac{- 18 0 ^{\circ} - 0.30469 \dots}{2}, x = - 6.13083 \dots, x = - 4.86473 \dots, x = - 9.27243 \dots, x = - 8.00632 \dots, x = - 12.41402 \dots, x = - 11.14792 \dots

Radians

x = 0.15234 \dots, x = \frac{π - 0.30469 \dots}{2}, x = - 2.98924 \dots, x = \frac{- π - 0.30469 \dots}{2}, x = - 6.13083 \dots, x = - 4.86473 \dots, x = - 9.27243 \dots, x = - 8.00632 \dots, x = - 12.41402 \dots, x = - 11.14792 \dots

Solution steps

sin (2 x) = 0.3, - 180 \circ \leq x \leq 18 0^{\circ}

Apply trig inverse properties

sin (2 x) = 0.3

General solutions for

sin (2 x) = 0.3

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

2 x = arcsin (0.3) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - arcsin (0.3) + 36 0^{\circ} n

2 x = arcsin (0.3) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - arcsin (0.3) + 36 0^{\circ} n

Solve

2 x = arcsin (0.3) + 36 0^{\circ} n : x = \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

2 x = arcsin (0.3) + 36 0^{\circ} n

Divide both sides by

2

2 x = arcsin (0.3) + 36 0^{\circ} n

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( 0.3 )}{2} + \frac{36 0 ^{\circ} n}{2}

Simplify

x = \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

Solve

2 x = 18 0^{\circ} - arcsin (0.3) + 36 0^{\circ} n : x = 9 0^{\circ} - \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

2 x = 18 0^{\circ} - arcsin (0.3) + 36 0^{\circ} n

Divide both sides by

2

2 x = 18 0^{\circ} - arcsin (0.3) + 36 0^{\circ} n

Divide both sides by

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{arcsin ( 0.3 )}{2} + \frac{36 0 ^{\circ} n}{2}

Simplify

x = 9 0^{\circ} - \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

x = 9 0^{\circ} - \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n, x = 9 0^{\circ} - \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

Solutions for the range

- 180 \circ \leq x \leq 18 0^{\circ}

x = 0.15234 \dots, x = \frac{18 0 ^{\circ} - 0.30469 \dots}{2}, x = - 2.98924 \dots, x = \frac{- 18 0 ^{\circ} - 0.30469 \dots}{2}, x = - 6.13083 \dots, x = - 4.86473 \dots, x = - 9.27243 \dots, x = - 8.00632 \dots, x = - 12.41402 \dots, x = - 11.14792 \dots

2^{c o t^{2} (x)} = 8

2 \cdot cos^{2} (x) + cos (x) - 1 = 0

cos (π y) = 0

cos (t) = - \frac{1}{3}

3 cot (x) - 1 = 0, 0 \leq x \leq 2 π x

What is the general solution for sin(2x)=0.3,-180\circ <= x<= 180 ?
The general solution for sin(2x)=0.3,-180\circ <= x<= 180 is