What is the value of ((6)^2sin^2(30))/(9.8) ?

The value of ((6)^2sin^2(30))/(9.8) is 45/49

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((6)^2sin^2(30))/(9.8)

\frac{( 6 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{9.8}

\frac{45}{49}

Decimal Notation

0.91836 \dots

Solution steps

\frac{( 6 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{9.8}

= \frac{6 ^{2} sin ^{2} ( 3 0 ^{\circ} )}{\frac{49}{5}}

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{6 ^{2} ( \frac{1}{2} ) ^{2}}{\frac{49}{5}}

Simplify

\frac{6 ^{2} ( \frac{1}{2} ) ^{2}}{\frac{49}{5}} : \frac{45}{49}

\frac{6 ^{2} ( \frac{1}{2} ) ^{2}}{\frac{49}{5}}

Apply the fraction rule:

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

= \frac{6 ^{2} ( \frac{1}{2} ) ^{2} \cdot 5}{49}

(\frac{1}{2})^{2} = \frac{1}{2 ^{2}}

(\frac{1}{2})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

Apply rule

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

= \frac{6 ^{2} \cdot 5 \cdot \frac{1}{2 ^{2}}}{49}

Multiply

6^{2} \cdot \frac{1}{2 ^{2}} \cdot 5 : 45

6^{2} \cdot \frac{1}{2 ^{2}} \cdot 5

Multiply fractions:

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

= \frac{1 \cdot 6 ^{2} \cdot 5}{2 ^{2}}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{6 ^{2} \cdot 5}{2 ^{2}}

Factor

6^{2} : 2^{2} \cdot 3^{2}

Factor

6 = 2 \cdot 3

= (2 \cdot 3)^{2}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

= 2^{2} \cdot 3^{2}

= \frac{2 ^{2} \cdot 3 ^{2} \cdot 5}{2 ^{2}}

Cancel the common factor:

2^{2}

= 3^{2} \cdot 5

3^{2} = 9

= 9 \cdot 5

Multiply the numbers:

9 \cdot 5 = 45

= 45

= \frac{45}{49}

= \frac{45}{49}

arctan (\frac{4}{6})

arcsin (- \frac{6}{7})

2 arcsin (1.5 \cdot sin (0.14))

\frac{sin ( 3 0 ^{\circ} ) + csc ( 3 0 ^{\circ} )}{sin ^{2} ( 3 0 ^{\circ} ) + cos ^{2} ( 6 0 ^{\circ} )}

\frac{cos ( 1 2 ^{\circ} )}{1.17}

What is the value of ((6)^2sin^2(30))/(9.8) ?
The value of ((6)^2sin^2(30))/(9.8) is 45/49