What is the general solution for cos(x+1)=-2/5 ?

The general solution for cos(x+1)=-2/5 is x=1.98231…+2pin-1,x=-1.98231…+2pin-1

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cos(x+1)=-2/5

cos (x + 1) = - \frac{2}{5}

x = 1.98231 \dots + 2 πn - 1, x = - 1.98231 \dots + 2 πn - 1

Degrees

x = 56.28239 \dots^{\circ} + 36 0^{\circ} n, x = - 170.87395 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (x + 1) = - \frac{2}{5}

Apply trig inverse properties

cos (x + 1) = - \frac{2}{5}

General solutions for

cos (x + 1) = - \frac{2}{5}

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

x + 1 = arccos (- \frac{2}{5}) + 2 πn, x + 1 = - arccos (- \frac{2}{5}) + 2 πn

x + 1 = arccos (- \frac{2}{5}) + 2 πn, x + 1 = - arccos (- \frac{2}{5}) + 2 πn

Solve

x + 1 = arccos (- \frac{2}{5}) + 2 πn : x = arccos (- \frac{2}{5}) + 2 πn - 1

x + 1 = arccos (- \frac{2}{5}) + 2 πn

Move

1

to the right side

x + 1 = arccos (- \frac{2}{5}) + 2 πn

Subtract

1

from both sides

x + 1 - 1 = arccos (- \frac{2}{5}) + 2 πn - 1

Simplify

x = arccos (- \frac{2}{5}) + 2 πn - 1

x = arccos (- \frac{2}{5}) + 2 πn - 1