What is the general solution for 5tan(x)sin(x)=-7sin(x) ?

The general solution for 5tan(x)sin(x)=-7sin(x) is x=2pin,x=pi+2pin,x=-0.95054…+pin

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Popular >

5tan(x)sin(x)=-7sin(x)

Solution

5 tan (x) sin (x) = - 7 sin (x)

Solution

x = 2 πn, x = π + 2 πn, x = - 0.95054 \dots + πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = - 54.46232 \dots^{\circ} + 18 0^{\circ} n

Solution steps

5 tan (x) sin (x) = - 7 sin (x)

Subtract

- 7 sin (x)

from both sides

5 tan (x) sin (x) + 7 sin (x) = 0

Factor

5 tan (x) sin (x) + 7 sin (x) : sin (x) (5 tan (x) + 7)

5 tan (x) sin (x) + 7 sin (x)

Factor out common term

sin (x)

= sin (x) (5 tan (x) + 7)

sin (x) (5 tan (x) + 7) = 0

Solving each part separately

sin (x) = 0 or 5 tan (x) + 7 = 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

5 tan (x) + 7 = 0 : x = arctan (- \frac{7}{5}) + πn

5 tan (x) + 7 = 0

Move

7

to the right side

5 tan (x) + 7 = 0

Subtract

7

from both sides

5 tan (x) + 7 - 7 = 0 - 7

Simplify

5 tan (x) = - 7

5 tan (x) = - 7

Divide both sides by

5

5 tan (x) = - 7

Divide both sides by

5

\frac{5 tan ( x )}{5} = \frac{- 7}{5}

Simplify

tan (x) = - \frac{7}{5}

tan (x) = - \frac{7}{5}

Apply trig inverse properties

tan (x) = - \frac{7}{5}

General solutions for

tan (x) = - \frac{7}{5}

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

x = arctan (- \frac{7}{5}) + πn

x = arctan (- \frac{7}{5}) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (- \frac{7}{5}) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = - 0.95054 \dots + πn

Popular Examples

tan(x+pi)-cos(x+pi/2)=0

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2cos^2(θ)-9cos(θ)+4=0

2 cos^{2} (θ) - 9 cos (θ) + 4 = 0

cos(2x+pi/4)=(sqrt(2))/2

cos (2 x + \frac{π}{4}) = \frac{2}{2}

solvefor x,tan(x)=1 solve for

x, tan (x) = 1

cot(t)=-sqrt(3)

cot (t) = - 3

Frequently Asked Questions (FAQ)

What is the general solution for 5tan(x)sin(x)=-7sin(x) ?
The general solution for 5tan(x)sin(x)=-7sin(x) is x=2pin,x=pi+2pin,x=-0.95054…+pin