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

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

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

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

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

Degrees

x = 48.18968 \dots^{\circ} + 36 0^{\circ} n, x = 311.81031 \dots^{\circ} + 36 0^{\circ} n

Solution steps

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

Divide both sides by

3

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

Divide both sides by

3

\frac{3 ( cos ( x ) - 1 )}{3} = \frac{- 1}{3}

Simplify

cos (x) - 1 = - \frac{1}{3}

cos (x) - 1 = - \frac{1}{3}

Move

1

to the right side

cos (x) - 1 = - \frac{1}{3}

Add

1

to both sides

cos (x) - 1 + 1 = - \frac{1}{3} + 1

Simplify

cos (x) - 1 + 1 = - \frac{1}{3} + 1

Simplify

cos (x) - 1 + 1 : cos (x)

cos (x) - 1 + 1

Add similar elements:

- 1 + 1 = 0

= cos (x)

Simplify

- \frac{1}{3} + 1 : \frac{2}{3}

- \frac{1}{3} + 1

Convert element to fraction:

1 = \frac{1 \cdot 3}{3}

= \frac{1 \cdot 3}{3} - \frac{1}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 \cdot 3 - 1}{3}

1 \cdot 3 - 1 = 2

1 \cdot 3 - 1

Multiply the numbers:

1 \cdot 3 = 3

= 3 - 1

Subtract the numbers:

3 - 1 = 2

= 2

= \frac{2}{3}

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

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

9.6 8^{2} = 12. 5^{2} + 6.4 7^{2} - 2 \cdot 12.5 \cdot 6.47 \cdot cos (θ)

- 4 = \frac{sin ( θ )}{cos ( θ )}

3 = cos (θ)

tan (θ) sin (θ) - 3 sin (θ) = 0

sin^{2} (x) = 1 - a^{2}

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