What is the value of sin(76)cos(31)-cos(76)sin(31) ?

The value of sin(76)cos(31)-cos(76)sin(31) is (sqrt(2))/2

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sin(76)cos(31)-cos(76)sin(31)

sin (7 6^{\circ}) cos (3 1^{\circ}) - cos (7 6^{\circ}) sin (3 1^{\circ})

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

sin (7 6^{\circ}) cos (3 1^{\circ}) - cos (7 6^{\circ}) sin (3 1^{\circ})

Rewrite using trig identities:

sin (4 5^{\circ})

sin (7 6^{\circ}) cos (3 1^{\circ}) - cos (7 6^{\circ}) sin (3 1^{\circ})

Use the Angle Difference identity:

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

= sin (7 6^{\circ} - 3 1^{\circ})

Simplify

= sin (4 5^{\circ})

= sin (4 5^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\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{2}{2}

= \frac{2}{2}

- 8 sec^{2} (0) tan (0) + 24 sec^{4} (0) tan (0)

csc (91 5^{\circ})

arctan (21)

arctan (27)

arctan (1)

What is the value of sin(76)cos(31)-cos(76)sin(31) ?
The value of sin(76)cos(31)-cos(76)sin(31) is (sqrt(2))/2