What is the general solution for 4cos^2(θ)-5cos(θ)=-4cos(θ)+3 ?

The general solution for 4cos^2(θ)-5cos(θ)=-4cos(θ)+3 is θ=2pin,θ=2.41885…+2pin,θ=-2.41885…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4cos^2(θ)-5cos(θ)=-4cos(θ)+3

4 cos^{2} (θ) - 5 cos (θ) = - 4 cos (θ) + 3

θ = 2 πn, θ = 2.41885 \dots + 2 πn, θ = - 2.41885 \dots + 2 πn

Solution steps

4 cos^{2} (θ) - 5 cos (θ) = - 4 cos (θ) + 3

Solve by substitution

cos (θ) = 1, cos (θ) = - \frac{3}{4}

cos (θ) = 1 : θ = 2 πn

cos (θ) = - \frac{3}{4} : θ = arccos (- \frac{3}{4}) + 2 πn, θ = - arccos (- \frac{3}{4}) + 2 πn

Combine all the solutions

θ = 2 πn, θ = arccos (- \frac{3}{4}) + 2 πn, θ = - arccos (- \frac{3}{4}) + 2 πn

Show solutions in decimal form

θ = 2 πn, θ = 2.41885 \dots + 2 πn, θ = - 2.41885 \dots + 2 πn

x, cos (x) = - 0.5

- 2 cos (x) = 3 sin (x)

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

20 = 15 cos (x) \cdot 2, 47

\frac{[ sin ( x ) + cos ( x ) ]}{cos ( x )} = sin (x) + 1

What is the general solution for 4cos^2(θ)-5cos(θ)=-4cos(θ)+3 ?
The general solution for 4cos^2(θ)-5cos(θ)=-4cos(θ)+3 is θ=2pin,θ=2.41885…+2pin,θ=-2.41885…+2pin