What is the value of (1)(1-10/100+1/(2pi)(sin(2pi)(10/100))) ?

The value of (1)(1-10/100+1/(2pi)(sin(2pi)(10/100))) is 9/10

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(1)(1-10/100+1/(2pi)(sin(2pi)(10/100)))

(1) (1 - \frac{10}{100} + \frac{1}{2 π} (sin (2 π) (\frac{10}{100})))

\frac{9}{10}

Decimal Notation

0.9

Solution steps

(1) (1 - \frac{10}{100} + \frac{1}{2 π} (sin (2 π) (\frac{10}{100})))

= 1 \cdot (1 - \frac{10}{100} + \frac{1}{2 π} sin (2 π) \frac{10}{100})

Rewrite using trig identities:

sin (2 π) = 0

sin (2 π)

sin (2 π) = sin (0)

sin (2 π)

Rewrite

2 π

2 π + 0

= sin (2 π + 0)

Apply the periodicity of

sin

sin (x + 2 π) = sin (x)

sin (2 π + 0) = sin (0)

= sin (0)

= sin (0)

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 0

= 1 \cdot (1 - \frac{10}{100} + \frac{1}{2 π} \cdot 0 \cdot \frac{10}{100})

Simplify

1 \cdot (1 - \frac{10}{100} + \frac{1}{2 π} \cdot 0 \cdot \frac{10}{100}) : \frac{9}{10}

1 \cdot (1 - \frac{10}{100} + \frac{1}{2 π} \cdot 0 \cdot \frac{10}{100})

\frac{10}{100} = \frac{1}{10}

\frac{10}{100}

Cancel the common factor:

10

= \frac{1}{10}

\frac{1}{2 π} \cdot 0 \cdot \frac{10}{100} = 0

\frac{1}{2 π} \cdot 0 \cdot \frac{10}{100}

\frac{10}{100} = \frac{1}{10}

\frac{10}{100}

Cancel the common factor:

10

= \frac{1}{10}

= 0 \cdot \frac{1}{2 π} \cdot \frac{1}{10}

Multiply fractions:

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

= 0 \cdot \frac{1 \cdot 1}{2 \cdot 10 π}

\frac{1 \cdot 1}{2 π 10} = \frac{1}{20 π}

\frac{1 \cdot 1}{2 π 10}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 10 π}

Multiply the numbers:

2 \cdot 10 = 20

= \frac{1}{20 π}

= 0 \cdot \frac{1}{20 π}

Apply rule

0 \cdot a = 0

= 0

= 1 \cdot (- \frac{1}{10} + 1 + 0)

Add the numbers:

1 + 0 = 1

= 1 \cdot (- \frac{1}{10} + 1)

Join

- \frac{1}{10} + 1 : \frac{9}{10}

- \frac{1}{10} + 1

Convert element to fraction:

1 = \frac{1 \cdot 10}{10}

= \frac{1 \cdot 10}{10} - \frac{1}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 10 - 1}{10}

1 \cdot 10 - 1 = 9

1 \cdot 10 - 1

Multiply the numbers:

1 \cdot 10 = 10

= 10 - 1

Subtract the numbers:

10 - 1 = 9

= 9

= \frac{9}{10}

= 1 \cdot \frac{9}{10}

Multiply:

1 \cdot \frac{9}{10} = \frac{9}{10}

= \frac{9}{10}

= \frac{9}{10}

cos (π) + i \cdot sin (π)

sin (\frac{3 π}{5}) cos (\frac{π}{15}) + cos (\frac{3 π}{5}) sin (\frac{π}{15})

arctan (\frac{6}{- 5})

4 sec (\frac{3 π}{4})

cos (\frac{π}{8}) + sin (\frac{π}{8})

What is the value of (1)(1-10/100+1/(2pi)(sin(2pi)(10/100))) ?
The value of (1)(1-10/100+1/(2pi)(sin(2pi)(10/100))) is 9/10