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 (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} : 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