What is the general solution for 3cos(θ)-1=0 ?

The general solution for 3cos(θ)-1=0 is θ=1.23095…+2pin,θ=2pi-1.23095…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3cos(θ)-1=0

3 cos (θ) - 1 = 0

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn

Degrees

θ = 70.52877 \dots^{\circ} + 36 0^{\circ} n, θ = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 cos (θ) - 1 = 0

Move

1

to the right side

3 cos (θ) - 1 = 0

Add

1

to both sides

3 cos (θ) - 1 + 1 = 0 + 1

Simplify

3 cos (θ) = 1

3 cos (θ) = 1

Divide both sides by

3

3 cos (θ) = 1

Divide both sides by

3

\frac{3 cos ( θ )}{3} = \frac{1}{3}

Simplify

cos (θ) = \frac{1}{3}

cos (θ) = \frac{1}{3}

Apply trig inverse properties

cos (θ) = \frac{1}{3}

General solutions for

cos (θ) = \frac{1}{3}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (\frac{1}{3}) + 2 πn, θ = 2 π - arccos (\frac{1}{3}) + 2 πn

θ = arccos (\frac{1}{3}) + 2 πn, θ = 2 π - arccos (\frac{1}{3}) + 2 πn

Show solutions in decimal form

θ = 1.23095 \dots + 2 πn, θ = 2 π - 1.23095 \dots + 2 πn

2 cos^{2} (θ) - cos (θ) = 0

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

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

cos (x) = - 1, 0 \leq x \leq 2 π

sin (x) tan^{2} (x) = sin (x)

What is the general solution for 3cos(θ)-1=0 ?
The general solution for 3cos(θ)-1=0 is θ=1.23095…+2pin,θ=2pi-1.23095…+2pin