What is the general solution for solvefor x,1.56sin(2x)=2*sin(x)cos(x) ?

The general solution for solvefor x,1.56sin(2x)=2*sin(x)cos(x) is x=pin,x= pi/2+pin

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solvefor x,1.56sin(2x)=2*sin(x)cos(x)

Solution

solve for

x, 1.56 sin (2 x) = 2 \cdot sin (x) cos (x)

Solution

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

1.56 sin (2 x) = 2 sin (x) cos (x)

Subtract

2 sin (x) cos (x)

from both sides

1.56 sin (2 x) - 2 sin (x) cos (x) = 0

Rewrite using trig identities

1.56 sin (2 x) - 2 cos (x) sin (x)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= 1.56 sin (2 x) - sin (2 x)

Simplify

= 0.56 sin (2 x)

0.56 sin (2 x) = 0

Multiply both sides by

100

0.56 sin (2 x) = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

0.56 sin (2 x) \cdot 100 = 0 \cdot 100

Refine

56 sin (2 x) = 0

56 sin (2 x) = 0

Divide both sides by

56

56 sin (2 x) = 0

Divide both sides by

56

\frac{56 sin ( 2 x )}{56} = \frac{0}{56}

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

Popular Examples

7/(sin(70))= 5/(sin(b))

\frac{7}{sin ( 7 0 ^{\circ} )} = \frac{5}{sin ( b )}

6cos^2(x)-7cos(x)+2=0

6 cos^{2} (x) - 7 cos (x) + 2 = 0

csc(θ)=(sqrt(20))/4

csc (θ) = \frac{20}{4}

sin(x+10)=cos(x+20)

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

c^2=b^2+a^2-2(b)(a)cos(θ)

c^{2} = b^{2} + a^{2} - 2 (b) (a) cos (θ)

Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,1.56sin(2x)=2*sin(x)cos(x) ?
The general solution for solvefor x,1.56sin(2x)=2*sin(x)cos(x) is x=pin,x= pi/2+pin