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

The general solution for 3sin(x)-2=7sin(x)-3 is x=0.25268…+2pin,x=pi-0.25268…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometry >

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

Solution

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

Solution

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

Degrees

x = 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 165.52248 \dots^{\circ} + 36 0^{\circ} n

Solution steps

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

Solve by substitution

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

Let:

sin (x) = u

3 u - 2 = 7 u - 3

3 u - 2 = 7 u - 3 : u = \frac{1}{4}

3 u - 2 = 7 u - 3

Move

2

to the right side

3 u - 2 = 7 u - 3

Add

2

to both sides

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

Simplify

3 u = 7 u - 1

3 u = 7 u - 1

Move

7 u

to the left side

3 u = 7 u - 1

Subtract

7 u

from both sides

3 u - 7 u = 7 u - 1 - 7 u

Simplify

- 4 u = - 1

- 4 u = - 1

Divide both sides by

- 4

- 4 u = - 1

Divide both sides by

- 4

\frac{- 4 u}{- 4} = \frac{- 1}{- 4}

Simplify

u = \frac{1}{4}

u = \frac{1}{4}

Substitute back

u = sin (x)

sin (x) = \frac{1}{4}

sin (x) = \frac{1}{4}

sin (x) = \frac{1}{4} : x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

sin (x) = \frac{1}{4}

Apply trig inverse properties

sin (x) = \frac{1}{4}

General solutions for

sin (x) = \frac{1}{4}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

Combine all the solutions

x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

Graph

Popular Examples

55^2=50^2+90^2-2*50*90*cos(x)

solvefor x,z=sin(2x+y)

7tan(x)=2sqrt(3)+tan(x),0<= θ<= 90

sin(X)=1

solvefor x,(17)/(sin(x))=(23)/(sin(75))

Frequently Asked Questions (FAQ)

What is the general solution for 3sin(x)-2=7sin(x)-3 ?
The general solution for 3sin(x)-2=7sin(x)-3 is x=0.25268…+2pin,x=pi-0.25268…+2pin