What is the value of 25sin(45) ?

The value of 25sin(45) is (25sqrt(2))/2

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25sin(45)

25 sin (4 5^{\circ})

\frac{25 2}{2}

Decimal Notation

17.67766 \dots

Solution steps

25 sin (4 5^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} 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}

= 25 \cdot \frac{2}{2}

Simplify

25 \cdot \frac{2}{2} : \frac{25 2}{2}

25 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 25}{2}

Apply radical rule:

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

= \frac{25 \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{25}{2 ^{1 - \frac{1}{2}}}

Subtract the numbers:

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

= \frac{25}{2 ^{\frac{1}{2}}}

Apply radical rule:

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

= \frac{25}{2}

Rationalize

\frac{25}{2} : \frac{25 2}{2}

\frac{25}{2}

Multiply by the conjugate

\frac{2}{2}

= \frac{25 2}{2 2}

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= \frac{25 2}{2}

= \frac{25 2}{2}

= \frac{25 2}{2}

sin (3) (0)

sin (3 0^{\circ}) cos (6 0^{\circ}) + sin (6 0^{\circ}) cos (3 0^{\circ})

csc (9)

cos (1) - cos (0)

sin^{3} (\frac{π}{6})