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

The value of sin(15)cos(15) is 1/4

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sin(15)cos(15)

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

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

Rewrite using trig identities:

\frac{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 (x) cos (x) = \frac{sin ( 2 x )}{2}

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

Simplify

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

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

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{\frac{1}{2}}{2}

Simplify

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

\frac{\frac{1}{2}}{2}

Apply the fraction rule:

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

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

= \frac{1}{4}

\frac{2 tan ( 1 5 ^{\circ} )}{1 - tan ^{2} ( 1 5 ^{\circ} )}

cos (1 π)

2 sin (\frac{5 π}{4})

arccos (\frac{1}{5})

tan (arctan (1))