What is the general solution for cos(x)=(sqrt(1+cos(x)))/2 ?

The general solution for cos(x)=(sqrt(1+cos(x)))/2 is x=0.87579…+2pin,x=2pi-0.87579…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(x)=(sqrt(1+cos(x)))/2

cos (x) = \frac{1 + cos ( x )}{2}

x = 0.87579 \dots + 2 πn, x = 2 π - 0.87579 \dots + 2 πn

Solution steps

cos (x) = \frac{1 + cos ( x )}{2}

Solve by substitution

cos (x) = \frac{1 + 17}{8}

cos (x) = \frac{1 + 17}{8} : x = arccos (\frac{1 + 17}{8}) + 2 πn, x = 2 π - arccos (\frac{1 + 17}{8}) + 2 πn

Combine all the solutions

x = arccos (\frac{1 + 17}{8}) + 2 πn, x = 2 π - arccos (\frac{1 + 17}{8}) + 2 πn

Show solutions in decimal form

x = 0.87579 \dots + 2 πn, x = 2 π - 0.87579 \dots + 2 πn

sin (\frac{x}{2}) + \frac{3}{2} = 0

cos (x) = 0.818

sin (x) = \frac{150}{212.6} (sin (11 5^{\circ}))

16 cos (2 θ) - 9 = 0

0 = 2 + 3 cos (θ) + cos (2 θ)

What is the general solution for cos(x)=(sqrt(1+cos(x)))/2 ?
The general solution for cos(x)=(sqrt(1+cos(x)))/2 is x=0.87579…+2pin,x=2pi-0.87579…+2pin