What is the value of (9810sin(120))/(sin(90)) ?

The value of (9810sin(120))/(sin(90)) is 4905sqrt(3)

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(9810sin(120))/(sin(90))

\frac{9810 sin ( 12 0 ^{\circ} )}{sin ( 9 0 ^{\circ} )}

49053

Decimal Notation

8495.70921 \dots

Solution steps

\frac{9810 sin ( 12 0 ^{\circ} )}{sin ( 9 0 ^{\circ} )}

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 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{3}{2}

Use the following trivial identity:

sin (9 0^{\circ}) = 1

sin (9 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}

= 1

= \frac{9810 \cdot \frac{3}{2}}{1}

Simplify

\frac{9810 \cdot \frac{3}{2}}{1} : 49053

\frac{9810 \cdot \frac{3}{2}}{1}

Multiply

9810 \cdot \frac{3}{2} : 49053

9810 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 9810}{2}

Divide the numbers:

\frac{9810}{2} = 4905

= 49053

= \frac{4905 3}{1}

Apply rule

\frac{a}{1} = a

= 49053

= 49053

e^{2 s i n (\frac{7 π}{6})}

tan (\frac{5 π}{9})

sin (2 arccos (\frac{2}{3}))

sin^{2} (\frac{2 π}{3}) + cos^{2} (\frac{2 π}{3})

\frac{72}{cos ( 16. 2 ^{\circ} )}

What is the value of (9810sin(120))/(sin(90)) ?
The value of (9810sin(120))/(sin(90)) is 4905sqrt(3)