What is the value of 6*0.5235sin(480) ?

The value of 6*0.5235sin(480) is (3141sqrt(3))/(2000)

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6*0.5235sin(480)

6 \cdot 0.5235 sin (48 0^{\circ})

\frac{3141 3}{2000}

Decimal Notation

2.72018 \dots

Solution steps

6 \cdot 0.5235 sin (48 0^{\circ})

= 6 \cdot \frac{1047}{2000} sin (48 0^{\circ})

Rewrite using trig identities:

sin (48 0^{\circ}) = \frac{3}{2}

sin (48 0^{\circ})

sin (48 0^{\circ}) = sin (12 0^{\circ})

sin (48 0^{\circ})

Rewrite

48 0^{\circ}

36 0^{\circ} + 12 0^{\circ}

= sin (36 0^{\circ} + 12 0^{\circ})

Apply the periodicity of

sin

sin (x + 36 0^{\circ}) = sin (x)

sin (36 0^{\circ} + 12 0^{\circ}) = sin (12 0^{\circ})

= sin (12 0^{\circ})

= sin (12 0^{\circ})

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 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{3}{2}

= \frac{3}{2}

= 6 \cdot \frac{1047}{2000} \cdot \frac{3}{2}

Simplify

6 \cdot \frac{1047}{2000} \cdot \frac{3}{2} : \frac{3141 3}{2000}

6 \cdot \frac{1047}{2000} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{1047 3 \cdot 6}{2000 \cdot 2}

Multiply the numbers:

1047 \cdot 6 = 6282

= \frac{6282 3}{2000 \cdot 2}

Multiply the numbers:

2000 \cdot 2 = 4000

= \frac{6282 3}{4000}

Cancel the common factor:

2

= \frac{3141 3}{2000}

= \frac{3141 3}{2000}

\frac{3}{cos ( 6 5 ^{\circ} )}

cos (0.875)

arctan (\frac{40}{20})

\frac{1}{2} sin (- \frac{π}{2})

3 (cos (12 0^{\circ}) + i sin (12 0^{\circ}))

What is the value of 6*0.5235sin(480) ?
The value of 6*0.5235sin(480) is (3141sqrt(3))/(2000)