What is the value of sin(15)cos(105)+cos(15)sin(105) ?

The value of sin(15)cos(105)+cos(15)sin(105) is (sqrt(3))/2

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sin(15)cos(105)+cos(15)sin(105)

sin (1 5^{\circ}) cos (10 5^{\circ}) + cos (1 5^{\circ}) sin (10 5^{\circ})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

sin (1 5^{\circ}) cos (10 5^{\circ}) + cos (1 5^{\circ}) sin (10 5^{\circ})

Rewrite using trig identities:

sin (12 0^{\circ})

sin (1 5^{\circ}) cos (10 5^{\circ}) + cos (1 5^{\circ}) sin (10 5^{\circ})

Use the Angle Sum identity:

sin (s) cos (t) + cos (s) sin (t) = sin (s + t)

= sin (1 5^{\circ} + 10 5^{\circ})

Simplify

= sin (12 0^{\circ})

= sin (12 0^{\circ})

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 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}

arctan (\frac{4}{12})

sin (13 2^{\circ})

4 sin (2)

sin (18 0^{\circ} - 4 5^{\circ})

- arctan (\frac{3}{4})

What is the value of sin(15)cos(105)+cos(15)sin(105) ?
The value of sin(15)cos(105)+cos(15)sin(105) is (sqrt(3))/2