What is the general solution for sin(x)tan(x-30)=0 ?

The general solution for sin(x)tan(x-30)=0 is x=360n,x=180+360n,x=180n+30

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sin(x)tan(x-30)=0

sin (x) tan (x - 3 0^{\circ}) = 0

x = 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} n + 3 0^{\circ}

Radians

x = 0 + 2 πn, x = π + 2 πn, x = \frac{π}{6} + πn

Solution steps

sin (x) tan (x - 3 0^{\circ}) = 0

Solving each part separately

sin (x) = 0 or tan (x - 3 0^{\circ}) = 0

sin (x) = 0 : x = 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

sin (x) = 0

General solutions for

sin (x) = 0

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

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

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

Solve

x = 0 + 36 0^{\circ} n : x = 36 0^{\circ} n

x = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

x = 36 0^{\circ} n

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

tan (x - 3 0^{\circ}) = 0 : x = 18 0^{\circ} n + 3 0^{\circ}

tan (x - 3 0^{\circ}) = 0

General solutions for

tan (x - 3 0^{\circ}) = 0

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x - 3 0^{\circ} = 0 + 18 0^{\circ} n

x - 3 0^{\circ} = 0 + 18 0^{\circ} n

Solve

x - 3 0^{\circ} = 0 + 18 0^{\circ} n : x = 18 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = 0 + 18 0^{\circ} n

0 + 18 0^{\circ} n = 18 0^{\circ} n

x - 3 0^{\circ} = 18 0^{\circ} n

Move

3 0^{\circ}

to the right side

x - 3 0^{\circ} = 18 0^{\circ} n

Add

3 0^{\circ}

to both sides

x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} n + 3 0^{\circ}

Simplify

x = 18 0^{\circ} n + 3 0^{\circ}

x = 18 0^{\circ} n + 3 0^{\circ}

x = 18 0^{\circ} n + 3 0^{\circ}

Combine all the solutions

x = 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} n + 3 0^{\circ}

- 4 tan^{2} (θ) = - 1

2 cos^{2} (x) + 5 sin (x) + 1 = 0

\frac{125}{sin ( 11 0 ^{\circ} )} = \frac{100}{sin ( b )}

tan (\frac{2 x}{3}) - 3 = 0

2 sin^{2} (x) - cos^{2} (x) - 2 = 0

What is the general solution for sin(x)tan(x-30)=0 ?
The general solution for sin(x)tan(x-30)=0 is x=360n,x=180+360n,x=180n+30