What is the value of (4*5*sin(150))/2 ?

The value of (4*5*sin(150))/2 is 5

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(45sin(150))/2

\frac{4 \cdot 5 \cdot sin ( 15 0 ^{\circ} )}{2}

5

Solution steps

\frac{4 \cdot 5 sin ( 15 0 ^{\circ} )}{2}

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 0^{\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{1}{2}

= \frac{4 \cdot 5 \cdot \frac{1}{2}}{2}

Simplify

\frac{4 \cdot 5 \cdot \frac{1}{2}}{2} : 5

\frac{4 \cdot 5 \cdot \frac{1}{2}}{2}

Multiply the numbers:

4 \cdot 5 = 20

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

Multiply

20 \cdot \frac{1}{2} : 10

20 \cdot \frac{1}{2}

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 20 = 20

= \frac{20}{2}

Divide the numbers:

\frac{20}{2} = 10

= 10

= \frac{10}{2}

Divide the numbers:

\frac{10}{2} = 5

= 5

= 5

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

30 sin (7 0^{\circ})

sin (- 4 0^{\circ})

\frac{7}{sin ( 4 0 ^{\circ} )}

\frac{1 + tan ( 1 5 ^{\circ} )}{1 - tan ( 1 5 ^{\circ} )}