What is the general solution for 4tan(x)sin(x)=3sin(x) ?

The general solution for 4tan(x)sin(x)=3sin(x) is x=2pin,x=pi+2pin,x=0.64350…+pin

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Popular >

4tan(x)sin(x)=3sin(x)

Solution

4 tan (x) sin (x) = 3 sin (x)

Solution

x = 2 πn, x = π + 2 πn, x = 0.64350 \dots + πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 36.86989 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 tan (x) sin (x) = 3 sin (x)

Subtract

3 sin (x)

from both sides

4 tan (x) sin (x) - 3 sin (x) = 0

Factor

4 tan (x) sin (x) - 3 sin (x) : sin (x) (4 tan (x) - 3)

4 tan (x) sin (x) - 3 sin (x)

Factor out common term

sin (x)

= sin (x) (4 tan (x) - 3)

sin (x) (4 tan (x) - 3) = 0

Solving each part separately

sin (x) = 0 or 4 tan (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

General solutions for

sin (x) = 0

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 = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

4 tan (x) - 3 = 0 : x = arctan (\frac{3}{4}) + πn

4 tan (x) - 3 = 0

Move

3

to the right side

4 tan (x) - 3 = 0

Add

3

to both sides

4 tan (x) - 3 + 3 = 0 + 3

Simplify

4 tan (x) = 3

4 tan (x) = 3

Divide both sides by

4

4 tan (x) = 3

Divide both sides by

4

\frac{4 tan ( x )}{4} = \frac{3}{4}

Simplify

tan (x) = \frac{3}{4}

tan (x) = \frac{3}{4}

Apply trig inverse properties

tan (x) = \frac{3}{4}

General solutions for

tan (x) = \frac{3}{4}

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{3}{4}) + πn

x = arctan (\frac{3}{4}) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (\frac{3}{4}) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 0.64350 \dots + πn

Popular Examples

sqrt(3)sin(θ)+cos(θ)=sqrt(3)

3 sin (θ) + cos (θ) = 3

25cos^2(θ)-9=0

25 cos^{2} (θ) - 9 = 0

sin(θ)=sqrt(3)cos(θ)

sin (θ) = 3 cos (θ)

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

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

-sin(θ)+cos(2θ)=1

- sin (θ) + cos (2 θ) = 1

Frequently Asked Questions (FAQ)

What is the general solution for 4tan(x)sin(x)=3sin(x) ?
The general solution for 4tan(x)sin(x)=3sin(x) is x=2pin,x=pi+2pin,x=0.64350…+pin