What is the value of (4+cos(2*(45)))*10^{-3} ?

The value of (4+cos(2*(45)))*10^{-3} is 1/250

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(4+cos(2(45)))10^{-3}

(4 + cos (2 \cdot (4 5^{\circ}))) \cdot 1 0^{- 3}

\frac{1}{250}

Decimal

0.004

Solution steps

(4 + cos (2 (4 5^{\circ}))) \cdot 1 0^{- 3}

= (4 + cos (2 \cdot 4 5^{\circ})) \cdot 1 0^{- 3}

Rewrite using trig identities:

cos (2 \cdot 4 5^{\circ}) = 0

cos (2 \cdot 4 5^{\circ})

Simplify

= cos (9 0^{\circ})

Use the following trivial identity:

cos (9 0^{\circ}) = 0

cos (9 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}

= 0

= 0

= (4 + 0) \cdot 1 0^{- 3}

Simplify

(4 + 0) \cdot 1 0^{- 3} : \frac{1}{250}

(4 + 0) \cdot 1 0^{- 3}

Add the numbers:

4 + 0 = 4

= 1 0^{- 3} \cdot 4

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

= 4 \cdot \frac{1}{1 0 ^{3}}

Multiply fractions:

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

= \frac{1 \cdot 4}{1 0 ^{3}}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{1 0 ^{3}}

Factor

4 : 2^{2}

Factor

4 = 2^{2}

Factor

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

Factor

10 = 2 \cdot 5

= (2 \cdot 5)^{3}

Apply exponent rule:

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

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

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

Cancel

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

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

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

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

Subtract the numbers:

3 - 2 = 1

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

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

5^{3} \cdot 2 = 250

5^{3} \cdot 2

5^{3} = 125

= 125 \cdot 2

Multiply the numbers:

125 \cdot 2 = 250

= 250

= \frac{1}{250}

= \frac{1}{250}

What is the value of (4+cos(2*(45)))*10^{-3} ?
The value of (4+cos(2*(45)))*10^{-3} is 1/250