What is the general solution for 10tan(x)sin(x)=sin(x) ?

The general solution for 10tan(x)sin(x)=sin(x) is x=2pin,x=pi+2pin,x=0.09966…+pin

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Popular >

10tan(x)sin(x)=sin(x)

Solution

10 tan (x) sin (x) = sin (x)

Solution

x = 2 πn, x = π + 2 πn, x = 0.09966 \dots + πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 5.71059 \dots^{\circ} + 18 0^{\circ} n

Solution steps

10 tan (x) sin (x) = sin (x)

Subtract

sin (x)

from both sides

10 tan (x) sin (x) - sin (x) = 0

Factor

10 tan (x) sin (x) - sin (x) : sin (x) (10 tan (x) - 1)

10 tan (x) sin (x) - sin (x)

Factor out common term

sin (x)

= sin (x) (10 tan (x) - 1)

sin (x) (10 tan (x) - 1) = 0

Solving each part separately

sin (x) = 0 or 10 tan (x) - 1 = 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

10 tan (x) - 1 = 0 : x = arctan (\frac{1}{10}) + πn

10 tan (x) - 1 = 0

Move

1

to the right side

10 tan (x) - 1 = 0

Add

1

to both sides

10 tan (x) - 1 + 1 = 0 + 1

Simplify

10 tan (x) = 1

10 tan (x) = 1

Divide both sides by

10

10 tan (x) = 1

Divide both sides by

10

\frac{10 tan ( x )}{10} = \frac{1}{10}

Simplify

tan (x) = \frac{1}{10}

tan (x) = \frac{1}{10}

Apply trig inverse properties

tan (x) = \frac{1}{10}

General solutions for

tan (x) = \frac{1}{10}

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

x = arctan (\frac{1}{10}) + πn

x = arctan (\frac{1}{10}) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (\frac{1}{10}) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 0.09966 \dots + πn

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Frequently Asked Questions (FAQ)

What is the general solution for 10tan(x)sin(x)=sin(x) ?
The general solution for 10tan(x)sin(x)=sin(x) is x=2pin,x=pi+2pin,x=0.09966…+pin