What is the general solution for (1.54)^2=2-2cos(x) ?

The general solution for (1.54)^2=2-2cos(x) is x=1.75768…+2pin,x=-1.75768…+2pin

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(1.54)^2=2-2cos(x)

(1.54)^{2} = 2 - 2 cos (x)

x = 1.75768 \dots + 2 πn, x = - 1.75768 \dots + 2 πn

Degrees

x = 100.70777 \dots^{\circ} + 36 0^{\circ} n, x = - 100.70777 \dots^{\circ} + 36 0^{\circ} n

Solution steps

(1.54)^{2} = 2 - 2 cos (x)

Switch sides

2 - 2 cos (x) = 1.5 4^{2}

1.5 4^{2} = 2.3716

2 - 2 cos (x) = 2.3716

Move

2

to the right side

2 - 2 cos (x) = 2.3716

Subtract

2

from both sides

2 - 2 cos (x) - 2 = 2.3716 - 2

Simplify

- 2 cos (x) = 0.3716

- 2 cos (x) = 0.3716

Divide both sides by

- 2

- 2 cos (x) = 0.3716

Divide both sides by

- 2

\frac{- 2 cos ( x )}{- 2} = \frac{0.3716}{- 2}

Simplify

cos (x) = - \frac{0.3716}{2}

cos (x) = - \frac{0.3716}{2}

Apply trig inverse properties

cos (x) = - \frac{0.3716}{2}

General solutions for

cos (x) = - \frac{0.3716}{2}

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

x = arccos (- \frac{0.3716}{2}) + 2 πn, x = - arccos (- \frac{0.3716}{2}) + 2 πn

x = arccos (- \frac{0.3716}{2}) + 2 πn, x = - arccos (- \frac{0.3716}{2}) + 2 πn

Show solutions in decimal form

x = 1.75768 \dots + 2 πn, x = - 1.75768 \dots + 2 πn

What is the general solution for (1.54)^2=2-2cos(x) ?
The general solution for (1.54)^2=2-2cos(x) is x=1.75768…+2pin,x=-1.75768…+2pin