What is the value of sin(85)cos(25)-sin(25)cos(85) ?

The value of sin(85)cos(25)-sin(25)cos(85) is (sqrt(3))/2

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sin(85)cos(25)-sin(25)cos(85)

sin (8 5^{\circ}) cos (2 5^{\circ}) - sin (2 5^{\circ}) cos (8 5^{\circ})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

sin (8 5^{\circ}) cos (2 5^{\circ}) - sin (2 5^{\circ}) cos (8 5^{\circ})

Rewrite as

= sin (8 5^{\circ}) cos (2 5^{\circ}) - cos (8 5^{\circ}) sin (2 5^{\circ})

Rewrite using trig identities:

sin (6 0^{\circ})

sin (8 5^{\circ}) cos (2 5^{\circ}) - cos (8 5^{\circ}) sin (2 5^{\circ})

Use the Angle Difference identity:

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

= sin (8 5^{\circ} - 2 5^{\circ})

Simplify

= sin (6 0^{\circ})

= sin (6 0^{\circ})

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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}

1 + 2 cos (π)

cos (2 \cdot \frac{3 π}{2})

9 sin (3 0^{\circ})

cos (- \frac{2}{5})

cos (\frac{\frac{4 π}{3}}{2})

What is the value of sin(85)cos(25)-sin(25)cos(85) ?
The value of sin(85)cos(25)-sin(25)cos(85) is (sqrt(3))/2