What is the value of pi(0.04)^2cos(30)(-0.2) ?

The value of pi(0.04)^2cos(30)(-0.2) is -(sqrt(3)pi)/(6250)

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pi(0.04)^2cos(30)(-0.2)

π (0.04)^{2} cos (3 0^{\circ}) (- 0.2)

- \frac{3 π}{6250}

Decimal Notation

- 0.00087 \dots

Solution steps

18 0^{\circ} (0.04)^{2} cos (3 0^{\circ}) (- 0.2)

= 18 0^{\circ} (\frac{1}{25})^{2} cos (3 0^{\circ}) (- \frac{1}{5})

Use the following trivial identity:

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

cos (3 0^{\circ})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= 18 0^{\circ} (\frac{1}{25})^{2} \frac{3}{2} (- \frac{1}{5})

Simplify

18 0^{\circ} (\frac{1}{25})^{2} \frac{3}{2} (- \frac{1}{5}) : - \frac{3 18 0 ^{\circ}}{6250}

18 0^{\circ} (\frac{1}{25})^{2} \frac{3}{2} (- \frac{1}{5})

Remove parentheses:

(- a) = - a

= - 18 0^{\circ} (\frac{1}{25})^{2} \frac{3}{2} \cdot \frac{1}{5}

(\frac{1}{25})^{2} = \frac{1}{2 5 ^{2}}

(\frac{1}{25})^{2}

Apply exponent rule:

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

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

Apply rule

1^{a} = 1

1^{2} = 1

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

= - 18 0^{\circ} \frac{1}{5} \cdot \frac{1}{2 5 ^{2}} \cdot \frac{3}{2}

Multiply fractions:

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

= - \frac{1 \cdot 3 \cdot 18 0 ^{\circ}}{2 5 ^{2} \cdot 2 \cdot 5}

Multiply:

1 \cdot 3 \cdot 18 0^{\circ} = 318 0^{\circ}

= - \frac{3 18 0 ^{\circ}}{2 5 ^{2} \cdot 2 \cdot 5}

Multiply the numbers:

2 \cdot 5 = 10

= - \frac{3 18 0 ^{\circ}}{2 5 ^{2} \cdot 10}

10 \cdot 2 5^{2} = 6250

10 \cdot 2 5^{2}

2 5^{2} = 625

= 10 \cdot 625

Multiply the numbers:

10 \cdot 625 = 6250

= 6250

= - \frac{3 18 0 ^{\circ}}{6250}

= - \frac{3 18 0 ^{\circ}}{6250}

- csc (3 0^{\circ})

6 sin (3)

5 cos (18 0^{\circ})

cos (17 5^{\circ})

arccos (0.7142)

What is the value of pi(0.04)^2cos(30)(-0.2) ?
The value of pi(0.04)^2cos(30)(-0.2) is -(sqrt(3)pi)/(6250)