What is the general solution for 7-6sin(x)=3+2sin(x) ?

The general solution for 7-6sin(x)=3+2sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

7-6sin(x)=3+2sin(x)

Solution

7 - 6 sin (x) = 3 + 2 sin (x)

Solution

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

7 - 6 sin (x) = 3 + 2 sin (x)

Solve by substitution

7 - 6 sin (x) = 3 + 2 sin (x)

Let:

sin (x) = u

7 - 6 u = 3 + 2 u

7 - 6 u = 3 + 2 u : u = \frac{1}{2}

7 - 6 u = 3 + 2 u

Move

7

to the right side

7 - 6 u = 3 + 2 u

Subtract

7

from both sides

7 - 6 u - 7 = 3 + 2 u - 7

Simplify

- 6 u = 2 u - 4

- 6 u = 2 u - 4

Move

2 u

to the left side

- 6 u = 2 u - 4

Subtract

2 u

from both sides

- 6 u - 2 u = 2 u - 4 - 2 u

Simplify

- 8 u = - 4

- 8 u = - 4

Divide both sides by

- 8

- 8 u = - 4

Divide both sides by

- 8

\frac{- 8 u}{- 8} = \frac{- 4}{- 8}

Simplify

\frac{- 8 u}{- 8} = \frac{- 4}{- 8}

Simplify

\frac{- 8 u}{- 8} : u

\frac{- 8 u}{- 8}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{8 u}{8}

Divide the numbers:

\frac{8}{8} = 1

= u

Simplify

\frac{- 4}{- 8} : \frac{1}{2}

\frac{- 4}{- 8}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{4}{8}

Cancel the common factor:

4

= \frac{1}{2}

u = \frac{1}{2}

u = \frac{1}{2}

u = \frac{1}{2}

Substitute back

u = sin (x)

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = \frac{1}{2}

General solutions for

sin (x) = \frac{1}{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}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Popular Examples

cos(θ)=(2*10^{-5})/(54*10^{-6)}

cos (θ) = \frac{2 \cdot 1 0 ^{- 5}}{54 \cdot 1 0 ^{- 6}}

sin(a)= 9/41

sin (a) = \frac{9}{41}

sin(x)= 10/300

sin (x) = \frac{10}{300}

cos^2(x)+2sin(x)=2

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

cos(216)=cos^2(a)-sin^2(a)

cos (21 6^{\circ}) = cos^{2} (a) - sin^{2} (a)

Frequently Asked Questions (FAQ)

What is the general solution for 7-6sin(x)=3+2sin(x) ?
The general solution for 7-6sin(x)=3+2sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin