What is the general solution for 14928=(18177)/((1+0.387cos(x))) ?

The general solution for 14928=(18177)/((1+0.387cos(x))) is x=0.97352…+2pin,x=2pi-0.97352…+2pin

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14928=(18177)/((1+0.387cos(x)))

14928 = \frac{18177}{( 1 + 0.387 cos ( x ) )}

x = 0.97352 \dots + 2 πn, x = 2 π - 0.97352 \dots + 2 πn

Solution steps

14928 = \frac{18177}{( 1 + 0.387 cos ( x ) )}

Switch sides

\frac{18177}{1 + 0.387 cos ( x )} = 14928

Multiply both sides by

1 + 0.387 cos (x)

18177 = 14928 (1 + 0.387 cos (x))

Switch sides

14928 (1 + 0.387 cos (x)) = 18177

Divide both sides by

14928

1 + 0.387 cos (x) = \frac{6059}{4976}

Move

1

to the right side

0.387 cos (x) = \frac{1083}{4976}

Divide both sides by

0.387

cos (x) = 0.56238 \dots

Verify Solutions

Find undefined (singularity) points:

cos (x) = - \frac{1000}{387}

Combine undefined points with solutions:

cos (x) = 0.56238 \dots

Apply trig inverse properties

x = arccos (0.56238 \dots) + 2 πn, x = 2 π - arccos (0.56238 \dots) + 2 πn

Show solutions in decimal form

x = 0.97352 \dots + 2 πn, x = 2 π - 0.97352 \dots + 2 πn

sin^{2} (θ) - 3 cos (θ) = 4

sec^{2} (x) - 2 = 0, 0 \leq x \leq 2 π

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

\frac{1}{2} = sin (2 θ)

1 - 2 sin (θ) = - 1

What is the general solution for 14928=(18177)/((1+0.387cos(x))) ?
The general solution for 14928=(18177)/((1+0.387cos(x))) is x=0.97352…+2pin,x=2pi-0.97352…+2pin