What is the general solution for 8cos(x+10)=5 ?

The general solution for 8cos(x+10)=5 is x=0.89566…+360n-10,x=360-0.89566…+360n-10

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8cos(x+10)=5

8 cos (x + 1 0^{\circ}) = 5

x = 0.89566 \dots + 36 0^{\circ} n - 1 0^{\circ}, x = 36 0^{\circ} - 0.89566 \dots + 36 0^{\circ} n - 1 0^{\circ}

Radians

x = 0.89566 \dots - \frac{π}{18} + 2 πn, x = 2 π - 0.89566 \dots - \frac{π}{18} + 2 πn

Solution steps

8 cos (x + 1 0^{\circ}) = 5

Divide both sides by

8

8 cos (x + 1 0^{\circ}) = 5

Divide both sides by

8

\frac{8 cos ( x + 1 0 ^{\circ} )}{8} = \frac{5}{8}

Simplify

cos (x + 1 0^{\circ}) = \frac{5}{8}

cos (x + 1 0^{\circ}) = \frac{5}{8}

Apply trig inverse properties

cos (x + 1 0^{\circ}) = \frac{5}{8}

General solutions for

cos (x + 1 0^{\circ}) = \frac{5}{8}

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

x + 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n, x + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n

x + 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n, x + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n

Solve

x + 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n : x = arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

x + 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n

Move

1 0^{\circ}

to the right side

x + 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n

Subtract

1 0^{\circ}

from both sides

x + 1 0^{\circ} - 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

Simplify

x = arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

x = arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

Solve

x + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

x + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n

Move

1 0^{\circ}

to the right side

x + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n

Subtract

1 0^{\circ}

from both sides

x + 1 0^{\circ} - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

Simplify

x = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

x = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

x = arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}, x = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

Show solutions in decimal form

x = 0.89566 \dots + 36 0^{\circ} n - 1 0^{\circ}, x = 36 0^{\circ} - 0.89566 \dots + 36 0^{\circ} n - 1 0^{\circ}

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

x, ln (y) + y^{2} = - cos (x)

tan (x) = 1.33

cot (x) = 5

8^{2} = 1 4^{2} + 1 9^{2} - 2 (14) (19) cos (C)

What is the general solution for 8cos(x+10)=5 ?
The general solution for 8cos(x+10)=5 is x=0.89566…+360n-10,x=360-0.89566…+360n-10