What is the general solution for cos(4+x)=0.45 ?

The general solution for cos(4+x)=0.45 is x=1.10403…+2pin-4,x=2pi-1.10403…+2pin-4

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cos(4+x)=0.45

cos (4 + x) = 0.45

x = 1.10403 \dots + 2 πn - 4, x = 2 π - 1.10403 \dots + 2 πn - 4

Degrees

x = - 165.92680 \dots^{\circ} + 36 0^{\circ} n, x = 67.56056 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (4 + x) = 0.45

Apply trig inverse properties

cos (4 + x) = 0.45

General solutions for

cos (4 + x) = 0.45

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

4 + x = arccos (0.45) + 2 πn, 4 + x = 2 π - arccos (0.45) + 2 πn

4 + x = arccos (0.45) + 2 πn, 4 + x = 2 π - arccos (0.45) + 2 πn

Solve

4 + x = arccos (0.45) + 2 πn : x = arccos (0.45) + 2 πn - 4

4 + x = arccos (0.45) + 2 πn

Move

4

to the right side

4 + x = arccos (0.45) + 2 πn

Subtract

4

from both sides

4 + x - 4 = arccos (0.45) + 2 πn - 4

Simplify

x = arccos (0.45) + 2 πn - 4

x = arccos (0.45) + 2 πn - 4