What is the general solution for 10cos(θ)-5sqrt(3)=0 ?

The general solution for 10cos(θ)-5sqrt(3)=0 is θ= pi/6+2pin,θ=(11pi)/6+2pin

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10cos(θ)-5sqrt(3)=0

10 cos (θ) - 53 = 0

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

10 cos (θ) - 53 = 0

Move

53

to the right side

10 cos (θ) - 53 = 0

Add

53

to both sides

10 cos (θ) - 53 + 53 = 0 + 53

Simplify

10 cos (θ) = 53

10 cos (θ) = 53

Divide both sides by

10

10 cos (θ) = 53

Divide both sides by

10

\frac{10 cos ( θ )}{10} = \frac{5 3}{10}

Simplify

cos (θ) = \frac{3}{2}

cos (θ) = \frac{3}{2}

General solutions for

cos (θ) = \frac{3}{2}

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

tan (θ) = \frac{8}{- 6}

tan (θ) = - 0.5

cos (x) \cdot sin (x) - 2 cos (x) = 0

sec (4 x) - \frac{2}{3} = 0

cos (θ) = 0.3, cos (2 θ)

What is the general solution for 10cos(θ)-5sqrt(3)=0 ?
The general solution for 10cos(θ)-5sqrt(3)=0 is θ= pi/6+2pin,θ=(11pi)/6+2pin