What is the value of 2sin(15)cos(15) ?

The value of 2sin(15)cos(15) is 1/2

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2sin(15)cos(15)

2 sin (1 5^{\circ}) cos (1 5^{\circ})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

2 sin (1 5^{\circ}) cos (1 5^{\circ})

Rewrite using trig identities:

sin (3 0^{\circ})

2 sin (1 5^{\circ}) cos (1 5^{\circ})

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= sin (2 \cdot 1 5^{\circ})

Simplify

= sin (3 0^{\circ})

= sin (3 0^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 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{1}{2}

2 sin (\frac{3 π}{2})

5 cos (0)

arcsin (sin (\frac{5 π}{3}))

cos (48 0^{\circ})

cos (\frac{4 π}{5})