What is the general solution for 29cos(x)=-17-cos(x) ?

The general solution for 29cos(x)=-17-cos(x) is x=2.17325…+2pin,x=-2.17325…+2pin

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29cos(x)=-17-cos(x)

29 cos (x) = - 17 - cos (x)

x = 2.17325 \dots + 2 πn, x = - 2.17325 \dots + 2 πn

Degrees

x = 124.51810 \dots^{\circ} + 36 0^{\circ} n, x = - 124.51810 \dots^{\circ} + 36 0^{\circ} n

Solution steps

29 cos (x) = - 17 - cos (x)

Solve by substitution

29 cos (x) = - 17 - cos (x)

Let:

cos (x) = u

29 u = - 17 - u

29 u = - 17 - u : u = - \frac{17}{30}

29 u = - 17 - u

Move

u

to the left side

29 u = - 17 - u

Add

u

to both sides

29 u + u = - 17 - u + u

Simplify

30 u = - 17

30 u = - 17

Divide both sides by

30

30 u = - 17

Divide both sides by

30

\frac{30 u}{30} = \frac{- 17}{30}

Simplify

u = - \frac{17}{30}

u = - \frac{17}{30}

Substitute back

u = cos (x)

cos (x) = - \frac{17}{30}

cos (x) = - \frac{17}{30}

cos (x) = - \frac{17}{30} : x = arccos (- \frac{17}{30}) + 2 πn, x = - arccos (- \frac{17}{30}) + 2 πn

cos (x) = - \frac{17}{30}

Apply trig inverse properties

cos (x) = - \frac{17}{30}

General solutions for

cos (x) = - \frac{17}{30}

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

x = arccos (- \frac{17}{30}) + 2 πn, x = - arccos (- \frac{17}{30}) + 2 πn

x = arccos (- \frac{17}{30}) + 2 πn, x = - arccos (- \frac{17}{30}) + 2 πn

Combine all the solutions

x = arccos (- \frac{17}{30}) + 2 πn, x = - arccos (- \frac{17}{30}) + 2 πn

Show solutions in decimal form

x = 2.17325 \dots + 2 πn, x = - 2.17325 \dots + 2 πn

2 cos (x) + 2 cos (2 x) = 0

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

tan (x) = \frac{- 3}{3}

tan (\frac{x}{3}) = \frac{3}{3}

12 sin^{2} (x) + sin (x) - 1 = 0

What is the general solution for 29cos(x)=-17-cos(x) ?
The general solution for 29cos(x)=-17-cos(x) is x=2.17325…+2pin,x=-2.17325…+2pin