What is the general solution for sin(2x)=(-2sqrt(6))/7 ?

The general solution for sin(2x)=(-2sqrt(6))/7 is x=-(0.77519…)/2+pin,x= pi/2+(0.77519…)/2+pin

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sin(2x)=(-2sqrt(6))/7

sin (2 x) = \frac{- 2 6}{7}

x = - \frac{0.77519 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.77519 \dots}{2} + πn

Degrees

x = - 22.20765 \dots^{\circ} + 18 0^{\circ} n, x = 112.20765 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x) = \frac{- 2 6}{7}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

sin (2 x) = - \frac{2 6}{7}

Apply trig inverse properties

sin (2 x) = - \frac{2 6}{7}

General solutions for

sin (2 x) = - \frac{2 6}{7}

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

2 x = arcsin (- \frac{2 6}{7}) + 2 πn, 2 x = π + arcsin (\frac{2 6}{7}) + 2 πn

2 x = arcsin (- \frac{2 6}{7}) + 2 πn, 2 x = π + arcsin (\frac{2 6}{7}) + 2 πn

Solve

2 x = arcsin (- \frac{2 6}{7}) + 2 πn : x = - \frac{arcsin ( \frac{2 6}{7} )}{2} + πn

2 x = arcsin (- \frac{2 6}{7}) + 2 πn

Simplify

arcsin (- \frac{2 6}{7}) + 2 πn : - arcsin (\frac{2 6}{7}) + 2 πn

arcsin (- \frac{2 6}{7}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2 6}{7}) = - arcsin (\frac{2 6}{7})

= - arcsin (\frac{2 6}{7}) + 2 πn

2 x = - arcsin (\frac{2 6}{7}) + 2 πn

Divide both sides by

2

2 x = - arcsin (\frac{2 6}{7}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arcsin ( \frac{2 6}{7} )}{2} + \frac{2 πn}{2}

Simplify

x = - \frac{arcsin ( \frac{2 6}{7} )}{2} + πn

x = - \frac{arcsin ( \frac{2 6}{7} )}{2} + πn

Solve

2 x = π + arcsin (\frac{2 6}{7}) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( \frac{2 6}{7} )}{2} + πn

2 x = π + arcsin (\frac{2 6}{7}) + 2 πn

Divide both sides by

2

2 x = π + arcsin (\frac{2 6}{7}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( \frac{2 6}{7} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} + \frac{arcsin ( \frac{2 6}{7} )}{2} + πn

x = \frac{π}{2} + \frac{arcsin ( \frac{2 6}{7} )}{2} + πn

x = - \frac{arcsin ( \frac{2 6}{7} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{2 6}{7} )}{2} + πn

Show solutions in decimal form

x = - \frac{0.77519 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.77519 \dots}{2} + πn

arctan (4 x) + arctan (6 x) = 90

2 sin (θ) tan (θ) - tan (θ) = 1 - 2 sin (θ)

7 cos (2 θ) - 9 = - 9 sin (θ)

1 - sin (x) = 3 cos (x)

tan (a) = \frac{8}{5}

What is the general solution for sin(2x)=(-2sqrt(6))/7 ?
The general solution for sin(2x)=(-2sqrt(6))/7 is x=-(0.77519…)/2+pin,x= pi/2+(0.77519…)/2+pin