What is the general solution for 7sin(x)+7sin(x)tan(x)=0 ?

The general solution for 7sin(x)+7sin(x)tan(x)=0 is x=2pin,x=pi+2pin,x=(3pi)/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

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

Factor

7 sin (x) + 7 sin (x) tan (x) : 7 sin (x) (tan (x) + 1)

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

Factor out common term

7 sin (x)

= 7 sin (x) (1 + tan (x))

7 sin (x) (tan (x) + 1) = 0

Solving each part separately

sin (x) = 0 or 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

tan (x) + 1 = 0 : x = \frac{3 π}{4} + πn

tan (x) + 1 = 0

Move

1

to the right side

tan (x) + 1 = 0

Subtract

1

from both sides

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

Simplify

tan (x) = - 1

tan (x) = - 1

General solutions for

tan (x) = - 1

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

Combine all the solutions

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

0 = cos (20 t) - cos (20.02 t)

2 tan (2 x - 10) = 3.4641

12 cos (\frac{π}{3} x) + 8 = 0

\frac{sin ( 4 5 ^{\circ} )}{497.01} = \frac{sin ( x )}{450}

\frac{35}{sin ( A )} = \frac{60}{sin ( 2 5 ^{\circ} )}

What is the general solution for 7sin(x)+7sin(x)tan(x)=0 ?
The general solution for 7sin(x)+7sin(x)tan(x)=0 is x=2pin,x=pi+2pin,x=(3pi)/4+pin