What is the general solution for sin^2(x)=((6m-5))/5 ?

The general solution for sin^2(x)=((6m-5))/5 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^2(x)=((6m-5))/5

sin^{2} (x) = \frac{( 6 m - 5 )}{5}

x = arcsin (\frac{6 m - 5}{5}) + 2 πn, x = π + arcsin (- \frac{6 m - 5}{5}) + 2 πn, x = arcsin (- \frac{6 m - 5}{5}) + 2 πn, x = π + arcsin (\frac{6 m - 5}{5}) + 2 πn

Solution steps

sin^{2} (x) = \frac{( 6 m - 5 )}{5}

Solve by substitution

sin^{2} (x) = \frac{6 m - 5}{5}

Let:

sin (x) = u

u^{2} = \frac{6 m - 5}{5}

u^{2} = \frac{6 m - 5}{5} : u = \frac{6 m - 5}{5}, u = - \frac{6 m - 5}{5}

u^{2} = \frac{6 m - 5}{5}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = \frac{6 m - 5}{5}, u = - \frac{6 m - 5}{5}

Substitute back

u = sin (x)

sin (x) = \frac{6 m - 5}{5}, sin (x) = - \frac{6 m - 5}{5}

sin (x) = \frac{6 m - 5}{5}, sin (x) = - \frac{6 m - 5}{5}

sin (x) = \frac{6 m - 5}{5} : x = arcsin (\frac{6 m - 5}{5}) + 2 πn, x = π + arcsin (- \frac{6 m - 5}{5}) + 2 πn

sin (x) = \frac{6 m - 5}{5}

Apply trig inverse properties

sin (x) = \frac{6 m - 5}{5}

General solutions for

sin (x) = \frac{6 m - 5}{5}

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

x = arcsin (\frac{6 m - 5}{5}) + 2 πn, x = π + arcsin (- \frac{6 m - 5}{5}) + 2 πn

x = arcsin (\frac{6 m - 5}{5}) + 2 πn, x = π + arcsin (- \frac{6 m - 5}{5}) + 2 πn

sin (x) = - \frac{6 m - 5}{5} : x = arcsin (- \frac{6 m - 5}{5}) + 2 πn, x = π + arcsin (\frac{6 m - 5}{5}) + 2 πn

sin (x) = - \frac{6 m - 5}{5}

Apply trig inverse properties

sin (x) = - \frac{6 m - 5}{5}

General solutions for

sin (x) = - \frac{6 m - 5}{5}

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

x = arcsin (- \frac{6 m - 5}{5}) + 2 πn, x = π + arcsin (\frac{6 m - 5}{5}) + 2 πn

x = arcsin (- \frac{6 m - 5}{5}) + 2 πn, x = π + arcsin (\frac{6 m - 5}{5}) + 2 πn

Combine all the solutions

x = arcsin (\frac{6 m - 5}{5}) + 2 πn, x = π + arcsin (- \frac{6 m - 5}{5}) + 2 πn, x = arcsin (- \frac{6 m - 5}{5}) + 2 πn, x = π + arcsin (\frac{6 m - 5}{5}) + 2 πn

sin^{2} (θ) - sin (θ) - 6 = 0

cos (2 θ) - 3 cos (θ) + 2 = 0

u, x = 2 tanh (u)

4 cos^{2} (x) + cos (2 x) - 7 cos (x) = - 2

4 cos (x) = 2 + 2 cos (x)

What is the general solution for sin^2(x)=((6m-5))/5 ?
The general solution for sin^2(x)=((6m-5))/5 is