What is the general solution for sin(2x)=((8m-8))/8 ?

The general solution for sin(2x)=((8m-8))/8 is x=(arcsin(m-1))/2+pin,x= pi/2+(arcsin(-m+1))/2+pin

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sin(2x)=((8m-8))/8

sin (2 x) = \frac{( 8 m - 8 )}{8}

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

Solution steps

sin (2 x) = \frac{( 8 m - 8 )}{8}

Simplify

\frac{8 m - 8}{8} : m - 1

\frac{8 m - 8}{8}

Factor

8 m - 8 : 8 (m - 1)

8 m - 8

Rewrite as

= 8 m - 8 \cdot 1

Factor out common term

8

= 8 (m - 1)

= \frac{8 ( m - 1 )}{8}

Divide the numbers:

\frac{8}{8} = 1

= m - 1

Apply trig inverse properties

sin (2 x) = m - 1

General solutions for

sin (2 x) = m - 1

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

2 x = arcsin (m - 1) + 2 πn, 2 x = π + arcsin (- m + 1) + 2 πn

2 x = arcsin (m - 1) + 2 πn, 2 x = π + arcsin (- m + 1) + 2 πn

Solve

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

2 x = arcsin (m - 1) + 2 πn

Divide both sides by

2

2 x = arcsin (m - 1) + 2 πn

Divide both sides by

2

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

Simplify

x = \frac{arcsin ( m - 1 )}{2} + πn

x = \frac{arcsin ( m - 1 )}{2} + πn

Solve

2 x = π + arcsin (- m + 1) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( - m + 1 )}{2} + πn

2 x = π + arcsin (- m + 1) + 2 πn

Divide both sides by

2

2 x = π + arcsin (- m + 1) + 2 πn

Divide both sides by

2

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

Simplify

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

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

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

sin (θ) = \frac{6}{5}

sin (θ) = 0.6367 + 0.1 \cdot cos (θ)

sec (x) + tan (x) = 3

cos (x) = \frac{10}{21}

cos (θ) = \frac{2}{3.3 8 ^{2} + 2 ^{2}}

What is the general solution for sin(2x)=((8m-8))/8 ?
The general solution for sin(2x)=((8m-8))/8 is x=(arcsin(m-1))/2+pin,x= pi/2+(arcsin(-m+1))/2+pin