What is the general solution for 13cos(C)-1=4cos(C)-8 ?

The general solution for 13cos(C)-1=4cos(C)-8 is C=2.46191…+2pin,C=-2.46191…+2pin

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13cos(C)-1=4cos(C)-8

13 cos (C) - 1 = 4 cos (C) - 8

C = 2.46191 \dots + 2 πn, C = - 2.46191 \dots + 2 πn

Solution steps

13 cos (C) - 1 = 4 cos (C) - 8

Solve by substitution

cos (C) = - \frac{7}{9}

cos (C) = - \frac{7}{9} : C = arccos (- \frac{7}{9}) + 2 πn, C = - arccos (- \frac{7}{9}) + 2 πn

Combine all the solutions

C = arccos (- \frac{7}{9}) + 2 πn, C = - arccos (- \frac{7}{9}) + 2 πn

Show solutions in decimal form

C = 2.46191 \dots + 2 πn, C = - 2.46191 \dots + 2 πn

sin (x) = - 0.2672

sin (x) = \frac{3}{10}

sin (2 x) = - \frac{2}{2}, 0 \leq x < 2 π

- 20 cos (θ) + 10 = 0

sin (x) - 1 = - 1

What is the general solution for 13cos(C)-1=4cos(C)-8 ?
The general solution for 13cos(C)-1=4cos(C)-8 is C=2.46191…+2pin,C=-2.46191…+2pin