What is the general solution for 2sin(x)+5sqrt(3)=6sqrt(3) ?

The general solution for 2sin(x)+5sqrt(3)=6sqrt(3) is x= pi/3+2pin,x=(2pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

2sin(x)+5sqrt(3)=6sqrt(3)

2 sin (x) + 53 = 63

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

Solution steps

2 sin (x) + 53 = 63

Move

53

to the right side

2 sin (x) + 53 = 63

Subtract

53

from both sides

2 sin (x) + 53 - 53 = 63 - 53

Simplify

2 sin (x) + 53 - 53 = 63 - 53

Simplify

2 sin (x) + 53 - 53 : 2 sin (x)

2 sin (x) + 53 - 53

Add similar elements:

53 - 53 = 0

= 2 sin (x)

Simplify

63 - 53 : 3

63 - 53

Add similar elements:

63 - 53 = 3

= 3

2 sin (x) = 3

2 sin (x) = 3

2 sin (x) = 3

Divide both sides by

2

2 sin (x) = 3

Divide both sides by

2

\frac{2 sin ( x )}{2} = \frac{3}{2}

Simplify

sin (x) = \frac{3}{2}

sin (x) = \frac{3}{2}

General solutions for

sin (x) = \frac{3}{2}

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

- 5 \cdot cos (x) - 8.6602500000000 \dots \cdot sin (x) = - 5

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

tan (\frac{x}{2} - \frac{π}{4}) = 3

53 tan (x) + 5 = 0

2 cot^{2} (x) = 6

What is the general solution for 2sin(x)+5sqrt(3)=6sqrt(3) ?
The general solution for 2sin(x)+5sqrt(3)=6sqrt(3) is x= pi/3+2pin,x=(2pi)/3+2pin