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

Solution steps

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

Divide both sides by

3

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

Move

1

to the right side

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

Apply trig inverse properties

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