What is the general solution for 3sin^2(x)-4cos(x)+1=0 ?

The general solution for 3sin^2(x)-4cos(x)+1=0 is x=0.84106…+2pin,x=2pi-0.84106…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3sin^2(x)-4cos(x)+1=0

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

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

4 - 3 cos^{2} (x) - 4 cos (x) = 0

Solve by substitution

cos (x) = - 2, cos (x) = \frac{2}{3}

cos (x) = - 2 :

No Solution

cos (x) = \frac{2}{3} : x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

Combine all the solutions

x = arccos (\frac{2}{3}) + 2 πn, x = 2 π - arccos (\frac{2}{3}) + 2 πn

Show solutions in decimal form

x = 0.84106 \dots + 2 πn, x = 2 π - 0.84106 \dots + 2 πn

sin (x) - cos (2 x) - 1 = 0

sin^{2} (x) = 3

x, c^{2} = a^{2} + b^{2} - 2 ab \cdot cos (x)

sin (- \frac{π}{8} c) = - \frac{14}{14}

\frac{25}{sin ( x )} = \frac{18}{sin ( 3 6 ^{\circ} )}

What is the general solution for 3sin^2(x)-4cos(x)+1=0 ?
The general solution for 3sin^2(x)-4cos(x)+1=0 is x=0.84106…+2pin,x=2pi-0.84106…+2pin