What is the value of 0.9144+3.048sin(30) ?

The value of 0.9144+3.048sin(30) is 1524/625

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Popular Trigonometry >

0.9144+3.048sin(30)

Solution

0.9144 + 3.048 sin (3 0^{\circ})

Solution

\frac{1524}{625}

Decimal

2.4384

Solution steps

0.9144 + 3.048 sin (3 0^{\circ})

= \frac{1143}{1250} + \frac{381}{125} sin (3 0^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 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}

= \frac{1}{2}

= \frac{1143}{1250} + \frac{381}{125} \cdot \frac{1}{2}

Simplify

\frac{1143}{1250} + \frac{381}{125} \cdot \frac{1}{2} : \frac{1524}{625}

\frac{1143}{1250} + \frac{381}{125} \cdot \frac{1}{2}

\frac{381}{125} \cdot \frac{1}{2} = \frac{381}{250}

\frac{381}{125} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{381 \cdot 1}{125 \cdot 2}

Multiply the numbers:

381 \cdot 1 = 381

= \frac{381}{125 \cdot 2}

Multiply the numbers:

125 \cdot 2 = 250

= \frac{381}{250}

= \frac{1143}{1250} + \frac{381}{250}

Least Common Multiplier of

1250, 250 : 1250

1250, 250

Least Common Multiplier (LCM)

Prime factorization of

1250 : 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

1250

1250

divides by

21250 = 625 \cdot 2

= 2 \cdot 625

625

divides by

5625 = 125 \cdot 5

= 2 \cdot 5 \cdot 125

125

divides by

5125 = 25 \cdot 5

= 2 \cdot 5 \cdot 5 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

Prime factorization of

250 : 2 \cdot 5 \cdot 5 \cdot 5

250

250

divides by

2250 = 125 \cdot 2

= 2 \cdot 125

125

divides by

5125 = 25 \cdot 5

= 2 \cdot 5 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 5 \cdot 5 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5 \cdot 5 \cdot 5

Multiply each factor the greatest number of times it occurs in either

1250

250

= 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

Multiply the numbers:

2 \cdot 5 \cdot 5 \cdot 5 \cdot 5 = 1250

= 1250

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

1250

For

\frac{381}{250} :

multiply the denominator and numerator by

5

\frac{381}{250} = \frac{381 \cdot 5}{250 \cdot 5} = \frac{1905}{1250}

= \frac{1143}{1250} + \frac{1905}{1250}

Since the denominators are equal, combine the fractions:

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

= \frac{1143 + 1905}{1250}

Add the numbers:

1143 + 1905 = 3048

= \frac{3048}{1250}

Cancel the common factor:

2

= \frac{1524}{625}

= \frac{1524}{625}

Popular Examples

(3(2)^2-sin(2))/(2e^2)

Frequently Asked Questions (FAQ)

What is the value of 0.9144+3.048sin(30) ?
The value of 0.9144+3.048sin(30) is 1524/625