What is the general solution for sec(x+10)=5.759 ?

The general solution for sec(x+10)=5.759 is x=1.39627…+360n-10,x=360-1.39627…+360n-10

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sec(x+10)=5.759

sec (x + 1 0^{\circ}) = 5.759

x = 1.39627 \dots + 36 0^{\circ} n - 1 0^{\circ}, x = 36 0^{\circ} - 1.39627 \dots + 36 0^{\circ} n - 1 0^{\circ}

Radians

x = 1.39627 \dots - \frac{π}{18} + 2 πn, x = 2 π - 1.39627 \dots - \frac{π}{18} + 2 πn

Solution steps

sec (x + 1 0^{\circ}) = 5.759

Apply trig inverse properties

sec (x + 1 0^{\circ}) = 5.759

General solutions for

sec (x + 1 0^{\circ}) = 5.759

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

x + 1 0^{\circ} = arcsec (5.759) + 36 0^{\circ} n, x + 1 0^{\circ} = 36 0^{\circ} - arcsec (5.759) + 36 0^{\circ} n

x + 1 0^{\circ} = arcsec (5.759) + 36 0^{\circ} n, x + 1 0^{\circ} = 36 0^{\circ} - arcsec (5.759) + 36 0^{\circ} n

Solve

x + 1 0^{\circ} = arcsec (5.759) + 36 0^{\circ} n : x = arcsec (5.759) + 36 0^{\circ} n - 1 0^{\circ}

x + 1 0^{\circ} = arcsec (5.759) + 36 0^{\circ} n

Move

1 0^{\circ}

to the right side

x + 1 0^{\circ} = arcsec (5.759) + 36 0^{\circ} n

Subtract

1 0^{\circ}

from both sides

x + 1 0^{\circ} - 1 0^{\circ} = arcsec (5.759) + 36 0^{\circ} n - 1 0^{\circ}

Simplify

x = arcsec (5.759) + 36 0^{\circ} n - 1 0^{\circ}

x = arcsec (5.759) + 36 0^{\circ} n - 1 0^{\circ}