What is the general solution for cos(a-5)=0.675 ?

The general solution for cos(a-5)=0.675 is a=0.82983…+2pin+5,a=2pi-0.82983…+2pin+5

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cos(a-5)=0.675

cos (a - 5) = 0.675

a = 0.82983 \dots + 2 πn + 5, a = 2 π - 0.82983 \dots + 2 πn + 5

Degrees

a = 334.02474 \dots^{\circ} + 36 0^{\circ} n, a = 598.93304 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (a - 5) = 0.675

Apply trig inverse properties

cos (a - 5) = 0.675

General solutions for

cos (a - 5) = 0.675

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

a - 5 = arccos (0.675) + 2 πn, a - 5 = 2 π - arccos (0.675) + 2 πn

a - 5 = arccos (0.675) + 2 πn, a - 5 = 2 π - arccos (0.675) + 2 πn

Solve

a - 5 = arccos (0.675) + 2 πn : a = arccos (0.675) + 2 πn + 5

a - 5 = arccos (0.675) + 2 πn

Move

5

to the right side

a - 5 = arccos (0.675) + 2 πn

Add

5

to both sides

a - 5 + 5 = arccos (0.675) + 2 πn + 5

Simplify

a = arccos (0.675) + 2 πn + 5

a = arccos (0.675) + 2 πn + 5

Solve

a - 5 = 2 π - arccos (0.675) + 2 πn : a = 2 π - arccos (0.675) + 2 πn + 5

a - 5 = 2 π - arccos (0.675) + 2 πn

Move

5

to the right side

a - 5 = 2 π - arccos (0.675) + 2 πn

Add

5

to both sides

a - 5 + 5 = 2 π - arccos (0.675) + 2 πn + 5

Simplify

a = 2 π - arccos (0.675) + 2 πn + 5

a = 2 π - arccos (0.675) + 2 πn + 5

a = arccos (0.675) + 2 πn + 5, a = 2 π - arccos (0.675) + 2 πn + 5

Show solutions in decimal form

a = 0.82983 \dots + 2 πn + 5, a = 2 π - 0.82983 \dots + 2 πn + 5

cos (7 a) = sin (a - 6)

sin^{5} (x) + 2 cos^{2} (x) = 1

cos^{3} (x) + sin^{2} (x) = 0

cos^{22} (x) + sin^{2} (x) - 1 = 0

sin (x) + cos (x) = 2 cos (x)

What is the general solution for cos(a-5)=0.675 ?
The general solution for cos(a-5)=0.675 is a=0.82983…+2pin+5,a=2pi-0.82983…+2pin+5