What is the general solution for (sin(180)}{20}=\frac{sin(a))/8 ?

The general solution for (sin(180)}{20}=\frac{sin(a))/8 is a=360n,a=180+360n

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Popular >

(sin(180)}{20}=\frac{sin(a))/8

Solution

\frac{sin ( 18 0 ^{\circ} )}{20} = \frac{sin ( a )}{8}

Solution

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

Radians

a = 0 + 2 πn, a = π + 2 πn

Solution steps

\frac{sin ( 18 0 ^{\circ} )}{20} = \frac{sin ( a )}{8}

sin (18 0^{\circ}) = 0

sin (18 0^{\circ})

Use the following trivial identity:

sin (18 0^{\circ}) = 0

sin (18 0^{\circ})

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}

= 0

= 0

\frac{0}{20} = \frac{sin ( a )}{8}

Switch sides

\frac{sin ( a )}{8} = \frac{0}{20}

Multiply both sides by

10

\frac{sin ( a )}{8} = \frac{0}{20}

Multiply both sides by

10

\frac{sin ( a )}{8} \cdot 10 = \frac{0}{20} \cdot 10

Simplify

\frac{sin ( a )}{8} \cdot 10 = \frac{0}{20} \cdot 10

Simplify

\frac{sin ( a )}{8} \cdot 10 : \frac{5 sin ( a )}{4}

\frac{sin ( a )}{8} \cdot 10

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{sin ( a ) \cdot 10}{8}

Cancel the common factor:

2

= \frac{5 sin ( a )}{4}

Simplify

\frac{0}{20} \cdot 10 : 0

\frac{0}{20} \cdot 10

Apply rule

\frac{0}{a} = 0, a \neq = 0

\frac{0}{20} = 0

= 0 \cdot 10

Apply rule

0 \cdot a = 0

= 0

\frac{5 sin ( a )}{4} = 0

\frac{5 sin ( a )}{4} = 0

\frac{5 sin ( a )}{4} = 0

Multiply both sides by

4

\frac{5 sin ( a )}{4} = 0

Multiply both sides by

4

\frac{4 \cdot 5 sin ( a )}{4} = 0 \cdot 4

Simplify

5 sin (a) = 0

5 sin (a) = 0

Divide both sides by

5

5 sin (a) = 0

Divide both sides by

5

\frac{5 sin ( a )}{5} = \frac{0}{5}

Simplify

sin (a) = 0

sin (a) = 0

General solutions for

sin (a) = 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}

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

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

Solve

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

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

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

a = 36 0^{\circ} n

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

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tan(4x)=12

tan (4 x) = 12

4csc(B)+5=0

4 csc (B) + 5 = 0

2cos(pi/5 x)=sqrt(3)

2 cos (\frac{π}{5} x) = 3

sin^2(x)+8sin(x)-1=0

sin^{2} (x) + 8 sin (x) - 1 = 0

Frequently Asked Questions (FAQ)

What is the general solution for (sin(180)}{20}=\frac{sin(a))/8 ?
The general solution for (sin(180)}{20}=\frac{sin(a))/8 is a=360n,a=180+360n