What is the value of 5*sin(pi/4) ?

The value of 5*sin(pi/4) is (5sqrt(2))/2

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5*sin(pi/4)

5 \cdot sin (\frac{π}{4})

\frac{5 2}{2}

Decimal Notation

3.53553 \dots

Solution steps

5 sin (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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}

= \frac{2}{2}

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

Simplify

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

5 \cdot \frac{2}{2}

Multiply fractions:

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

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

Apply radical rule:

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

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

Apply exponent rule:

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

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

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

Subtract the numbers:

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

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

Apply radical rule:

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

= \frac{5}{2}

Rationalize

\frac{5}{2} : \frac{5 2}{2}

\frac{5}{2}

Multiply by the conjugate

\frac{2}{2}

= \frac{5 2}{2 2}

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= \frac{5 2}{2}

= \frac{5 2}{2}

= \frac{5 2}{2}

- arctan (\frac{20}{200})

(\frac{sin ( 2 ) ( \frac{π}{2} )}{2}) - (\frac{sin ( 2 ) ( \frac{π}{4} )}{2})

arccos (- 2.31)

\frac{sin ( 3 0 ^{\circ} ) \cdot cos ( 6 0 ^{\circ} ) \cdot csc ( 4 5 ^{\circ} )}{tan ( 3 0 ^{\circ} ) \cdot sec ( 6 0 ^{\circ} ) \cdot cot ( 4 5 ^{\circ} )}

tan^{2} (4 5^{\circ} - \frac{34}{2})