What is the general solution for sin(2x+64)=(sqrt(3))/2 ?

The general solution for sin(2x+64)=(sqrt(3))/2 is x=-32+pin+pi/6 ,x=-32+pin+pi/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2x+64)=(sqrt(3))/2

Solution

sin (2 x + 64) = \frac{3}{2}

Solution

x = - 32 + πn + \frac{π}{6}, x = - 32 + πn + \frac{π}{3}

Degrees

x = - 1803.46494 \dots^{\circ} + 18 0^{\circ} n, x = - 1773.46494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x + 64) = \frac{3}{2}

General solutions for

sin (2 x + 64) = \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}

2 x + 64 = \frac{π}{3} + 2 πn, 2 x + 64 = \frac{2 π}{3} + 2 πn

2 x + 64 = \frac{π}{3} + 2 πn, 2 x + 64 = \frac{2 π}{3} + 2 πn

Solve

2 x + 64 = \frac{π}{3} + 2 πn : x = - 32 + πn + \frac{π}{6}

2 x + 64 = \frac{π}{3} + 2 πn

Move

64

to the right side

2 x + 64 = \frac{π}{3} + 2 πn

Subtract

64

from both sides

2 x + 64 - 64 = \frac{π}{3} + 2 πn - 64

Simplify

2 x = \frac{π}{3} + 2 πn - 64

2 x = \frac{π}{3} + 2 πn - 64

Divide both sides by

2

2 x = \frac{π}{3} + 2 πn - 64

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{2 πn}{2} - \frac{64}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{2 πn}{2} - \frac{64}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2} - \frac{64}{2} : - 32 + πn + \frac{π}{6}

\frac{\frac{π}{3}}{2} + \frac{2 πn}{2} - \frac{64}{2}

Group like terms

= - \frac{64}{2} + \frac{2 πn}{2} + \frac{\frac{π}{3}}{2}

\frac{64}{2} = 32

\frac{64}{2}

Divide the numbers:

\frac{64}{2} = 32

= 32

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

= - 32 + πn + \frac{π}{6}

x = - 32 + πn + \frac{π}{6}

x = - 32 + πn + \frac{π}{6}

x = - 32 + πn + \frac{π}{6}

Solve

2 x + 64 = \frac{2 π}{3} + 2 πn : x = - 32 + πn + \frac{π}{3}

2 x + 64 = \frac{2 π}{3} + 2 πn

Move

64

to the right side

2 x + 64 = \frac{2 π}{3} + 2 πn

Subtract

64

from both sides

2 x + 64 - 64 = \frac{2 π}{3} + 2 πn - 64

Simplify

2 x = \frac{2 π}{3} + 2 πn - 64

2 x = \frac{2 π}{3} + 2 πn - 64

Divide both sides by

2

2 x = \frac{2 π}{3} + 2 πn - 64

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2} - \frac{64}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2} - \frac{64}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2} - \frac{64}{2} : - 32 + πn + \frac{π}{3}

\frac{\frac{2 π}{3}}{2} + \frac{2 πn}{2} - \frac{64}{2}

Group like terms

= - \frac{64}{2} + \frac{2 πn}{2} + \frac{\frac{2 π}{3}}{2}

\frac{64}{2} = 32

\frac{64}{2}

Divide the numbers:

\frac{64}{2} = 32

= 32

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{2 π}{3}}{2} = \frac{π}{3}

\frac{\frac{2 π}{3}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{2 π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{2 π}{6}

Cancel the common factor:

2

= \frac{π}{3}

= - 32 + πn + \frac{π}{3}

x = - 32 + πn + \frac{π}{3}

x = - 32 + πn + \frac{π}{3}

x = - 32 + πn + \frac{π}{3}

x = - 32 + πn + \frac{π}{6}, x = - 32 + πn + \frac{π}{3}

Popular Examples

sin(θ)=0,6

sin (θ) = 0, 6

sin(x)=sin(pi/2)

sin (x) = sin (\frac{π}{2})

(sin(x))/(1-cos^2(x))=sec(x)

\frac{sin ( x )}{1 - cos ^{2} ( x )} = sec (x)

cos(2x)-2sin(x)=1,0<x<= 360

cos (2 x) - 2 sin (x) = 1, 0^{\circ} < x \leq 36 0^{\circ}

cos(api)-1=0

cos (aπ) - 1 = 0

Frequently Asked Questions (FAQ)

What is the general solution for sin(2x+64)=(sqrt(3))/2 ?
The general solution for sin(2x+64)=(sqrt(3))/2 is x=-32+pin+pi/6 ,x=-32+pin+pi/3