What is the general solution for 1/2 (1+cos(x))=0.6294095226 ?

The general solution for 1/2 (1+cos(x))=0.6294095226 is x=1.30899…+2pin,x=2pi-1.30899…+2pin

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1/2 (1+cos(x))=0.6294095226

\frac{1}{2} (1 + cos (x)) = 0.6294095226

x = 1.30899 \dots + 2 πn, x = 2 π - 1.30899 \dots + 2 πn

Degrees

x = 74.99999 \dots^{\circ} + 36 0^{\circ} n, x = 285.00000 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{1}{2} (1 + cos (x)) = 0.6294095226

Multiply both sides by

2

\frac{1}{2} (1 + cos (x)) = 0.6294095226

Multiply both sides by

2

2 \cdot \frac{1}{2} (1 + cos (x)) = 0.6294095226 \cdot 2

Simplify

1 + cos (x) = 1.25881 \dots

1 + cos (x) = 1.25881 \dots

Move

1

to the right side

1 + cos (x) = 1.25881 \dots

Subtract

1

from both sides

1 + cos (x) - 1 = 1.25881 \dots - 1

Simplify

cos (x) = 0.2588190452

cos (x) = 0.2588190452

Apply trig inverse properties

cos (x) = 0.2588190452

General solutions for

cos (x) = 0.2588190452

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

x = arccos (0.2588190452) + 2 πn, x = 2 π - arccos (0.2588190452) + 2 πn

x = arccos (0.2588190452) + 2 πn, x = 2 π - arccos (0.2588190452) + 2 πn

Show solutions in decimal form

x = 1.30899 \dots + 2 πn, x = 2 π - 1.30899 \dots + 2 πn

2 + 2 cos (x) = 6 cos (x)

120 = 120 sin (\frac{π}{3} c)

2 sin^{2} (x) + cos (x) - 3 = 0

cot (x) cos^{2} (x) = 2 cot (x), 0 \leq x \leq 2 π

2 cot^{2} (3 θ) = 5 csc (3 θ) - 4

What is the general solution for 1/2 (1+cos(x))=0.6294095226 ?
The general solution for 1/2 (1+cos(x))=0.6294095226 is x=1.30899…+2pin,x=2pi-1.30899…+2pin