What is the general solution for 10cos(x)-5sqrt(2)=0 ?

The general solution for 10cos(x)-5sqrt(2)=0 is x= pi/4+2pin,x=(7pi)/4+2pin

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10cos(x)-5sqrt(2)=0

10 cos (x) - 52 = 0

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Degrees

x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n

Solution steps

10 cos (x) - 52 = 0

Move

52

to the right side

10 cos (x) - 52 = 0

Add

52

to both sides

10 cos (x) - 52 + 52 = 0 + 52

Simplify

10 cos (x) = 52

10 cos (x) = 52

Divide both sides by

10

10 cos (x) = 52

Divide both sides by

10

\frac{10 cos ( x )}{10} = \frac{5 2}{10}

Simplify

cos (x) = \frac{2}{2}

cos (x) = \frac{2}{2}

General solutions for

cos (x) = \frac{2}{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}

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sin (2 x) = sin^{2} (2 x)

- 8 sin (2 θ + 4 5^{\circ}) = - 4, 0 \leq x < 36 0^{\circ}

sin (b) = \frac{10.21 ( sin ( 61.3 6 ^{\circ} ) )}{11.47}

cos (θ) = 0.513

cot (x) = - \frac{24}{7}

What is the general solution for 10cos(x)-5sqrt(2)=0 ?
The general solution for 10cos(x)-5sqrt(2)=0 is x= pi/4+2pin,x=(7pi)/4+2pin