What is the value of sin(72)cos(42)-cos(72)sin(42) ?

The value of sin(72)cos(42)-cos(72)sin(42) is 1/2

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sin(72)cos(42)-cos(72)sin(42)

sin (7 2^{\circ}) cos (4 2^{\circ}) - cos (7 2^{\circ}) sin (4 2^{\circ})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

sin (7 2^{\circ}) cos (4 2^{\circ}) - cos (7 2^{\circ}) sin (4 2^{\circ})

Rewrite using trig identities:

sin (3 0^{\circ})

sin (7 2^{\circ}) cos (4 2^{\circ}) - cos (7 2^{\circ}) sin (4 2^{\circ})

Use the Angle Difference identity:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= sin (7 2^{\circ} - 4 2^{\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}

35 sin (4 0^{\circ})

tan (- \frac{23 π}{6})

sin (2) (2 π)

\frac{1}{tan ( 3 6 ^{\circ} )}

arccsc (- \frac{6}{5})

What is the value of sin(72)cos(42)-cos(72)sin(42) ?
The value of sin(72)cos(42)-cos(72)sin(42) is 1/2