What is the general solution for 4cos^2(x)-5cos(x)+1=0 ?

The general solution for 4cos^2(x)-5cos(x)+1=0 is x=2pin,x=1.31811…+2pin,x=2pi-1.31811…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4cos^2(x)-5cos(x)+1=0

4 cos^{2} (x) - 5 cos (x) + 1 = 0

x = 2 πn, x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

Solution steps

4 cos^{2} (x) - 5 cos (x) + 1 = 0

Solve by substitution

cos (x) = 1, cos (x) = \frac{1}{4}

cos (x) = 1 : x = 2 πn

cos (x) = \frac{1}{4} : x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

Combine all the solutions

x = 2 πn, x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

cos (x + 6 0^{\circ}) = sin (x)

csc^{2} (x) = 2 cot^{2} (x)

2 sin^{2} (x) + sin (2 x) = 0

5 sin (x) cos (x) + 4 cos (x) = 0

2 sin (x) = 4 cos (x)

What is the general solution for 4cos^2(x)-5cos(x)+1=0 ?
The general solution for 4cos^2(x)-5cos(x)+1=0 is x=2pin,x=1.31811…+2pin,x=2pi-1.31811…+2pin