What is the general solution for 7sin(2X)=0 ?

The general solution for 7sin(2X)=0 is X=pin,X= pi/2+pin

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7sin(2X)=0

7 sin (2 X) = 0

X = πn, X = \frac{π}{2} + πn

Degrees

X = 0^{\circ} + 18 0^{\circ} n, X = 9 0^{\circ} + 18 0^{\circ} n

Solution steps

7 sin (2 X) = 0

Divide both sides by

7

7 sin (2 X) = 0

Divide both sides by

7

\frac{7 sin ( 2 X )}{7} = \frac{0}{7}

Simplify

sin (2 X) = 0

sin (2 X) = 0

General solutions for

sin (2 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}

2 X = 0 + 2 πn, 2 X = π + 2 πn

2 X = 0 + 2 πn, 2 X = π + 2 πn

Solve

2 X = 0 + 2 πn : X = πn

2 X = 0 + 2 πn

0 + 2 πn = 2 πn

2 X = 2 πn

Divide both sides by

2

2 X = 2 πn

Divide both sides by

2

\frac{2 X}{2} = \frac{2 πn}{2}

Simplify

X = πn

X = πn

Solve

2 X = π + 2 πn : X = \frac{π}{2} + πn

2 X = π + 2 πn

Divide both sides by

2

2 X = π + 2 πn

Divide both sides by

2

\frac{2 X}{2} = \frac{π}{2} + \frac{2 πn}{2}

Simplify

X = \frac{π}{2} + πn

X = \frac{π}{2} + πn

X = πn, X = \frac{π}{2} + πn

sec (- \frac{π}{6})

sin (x) (tan (x)) = sec (x) - cos (x)

cos (θ) = 0

arctan (- \frac{3}{3})

sec (1)

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