What is the general solution for cos(30+u)=0.8177 ?

The general solution for cos(30+u)=0.8177 is u=0.61339…+360n-30,u=360-0.61339…+360n-30

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cos(30+u)=0.8177

cos (3 0^{\circ} + u) = 0.8177

u = 0.61339 \dots + 36 0^{\circ} n - 3 0^{\circ}, u = 36 0^{\circ} - 0.61339 \dots + 36 0^{\circ} n - 3 0^{\circ}

Radians

u = 0.61339 \dots - \frac{π}{6} + 2 πn, u = 2 π - 0.61339 \dots - \frac{π}{6} + 2 πn

Solution steps

cos (3 0^{\circ} + u) = 0.8177

Apply trig inverse properties

cos (3 0^{\circ} + u) = 0.8177

General solutions for

cos (3 0^{\circ} + u) = 0.8177

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

3 0^{\circ} + u = arccos (0.8177) + 36 0^{\circ} n, 3 0^{\circ} + u = 36 0^{\circ} - arccos (0.8177) + 36 0^{\circ} n

3 0^{\circ} + u = arccos (0.8177) + 36 0^{\circ} n, 3 0^{\circ} + u = 36 0^{\circ} - arccos (0.8177) + 36 0^{\circ} n

Solve

3 0^{\circ} + u = arccos (0.8177) + 36 0^{\circ} n : u = arccos (0.8177) + 36 0^{\circ} n - 3 0^{\circ}

3 0^{\circ} + u = arccos (0.8177) + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

3 0^{\circ} + u = arccos (0.8177) + 36 0^{\circ} n

Subtract

3 0^{\circ}

from both sides

3 0^{\circ} + u - 3 0^{\circ} = arccos (0.8177) + 36 0^{\circ} n - 3 0^{\circ}

Simplify

u = arccos (0.8177) + 36 0^{\circ} n - 3 0^{\circ}

u = arccos (0.8177) + 36 0^{\circ} n - 3 0^{\circ}