What is the value of -(0.3^2(sec^3(60)))/(0.2) ?

The value of -(0.3^2(sec^3(60)))/(0.2) is -18/5

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-(0.3^2(sec^3(60)))/(0.2)

- \frac{0. 3 ^{2} ( sec ^{3} ( 6 0 ^{\circ} ) )}{0.2}

- \frac{18}{5}

Decimal Notation

- 3.6

Solution steps

- \frac{0. 3 ^{2} ( sec ^{3} ( 6 0 ^{\circ} ) )}{0.2}

= - \frac{( \frac{3}{10} ) ^{2} sec ^{3} ( 6 0 ^{\circ} )}{\frac{1}{5}}

Use the following trivial identity:

sec (6 0^{\circ}) = 2

sec (6 0^{\circ})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

= - \frac{( \frac{3}{10} ) ^{2} \cdot 2 ^{3}}{\frac{1}{5}}

Simplify

- \frac{( \frac{3}{10} ) ^{2} \cdot 2 ^{3}}{\frac{1}{5}} : - \frac{18}{5}

- \frac{( \frac{3}{10} ) ^{2} \cdot 2 ^{3}}{\frac{1}{5}}

Apply the fraction rule:

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

= - \frac{2 ^{3} \cdot 5 ( \frac{3}{10} ) ^{2}}{1}

(\frac{3}{10})^{2} = \frac{3 ^{2}}{1 0 ^{2}}

(\frac{3}{10})^{2}

Apply exponent rule:

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

= \frac{3 ^{2}}{1 0 ^{2}}

= - \frac{2 ^{3} \cdot 5 \cdot \frac{3 ^{2}}{1 0 ^{2}}}{1}

Multiply

\frac{3 ^{2}}{1 0 ^{2}} \cdot 2^{3} \cdot 5 : \frac{18}{5}

\frac{3 ^{2}}{1 0 ^{2}} \cdot 2^{3} \cdot 5

Multiply fractions:

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

= \frac{3 ^{2} \cdot 2 ^{3} \cdot 5}{1 0 ^{2}}

Factor

1 0^{2} : 2^{2} \cdot 5^{2}

Factor

10 = 2 \cdot 5

= (2 \cdot 5)^{2}

Apply exponent rule:

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

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

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

Cancel

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

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

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{3}}{2 ^{2}} = 2^{3 - 2}

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

Subtract the numbers:

3 - 2 = 1

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

Cancel the common factor:

5

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

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

3^{2} \cdot 2 = 18

3^{2} \cdot 2

3^{2} = 9

= 9 \cdot 2

Multiply the numbers:

9 \cdot 2 = 18

= 18

= \frac{18}{5}

= - \frac{\frac{18}{5}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= - \frac{18}{5}

= - \frac{18}{5}

ln (cosh (2 + 5 i))

\frac{3 ( 6 ) ^{2} - sin ( 6 )}{2 e ^{6}}

arctan (\frac{0.00346}{11.93})

\frac{1}{2} + sin (\frac{π}{2})

- sin (\frac{3}{4} π)

What is the value of -(0.3^2(sec^3(60)))/(0.2) ?
The value of -(0.3^2(sec^3(60)))/(0.2) is -18/5