What is the value of sin(330)cos(30)-cos(330)sin(30) ?

The value of sin(330)cos(30)-cos(330)sin(30) is -(sqrt(3))/2

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sin(330)cos(30)-cos(330)sin(30)

sin (33 0^{\circ}) cos (3 0^{\circ}) - cos (33 0^{\circ}) sin (3 0^{\circ})

- \frac{3}{2}

Solution steps

sin (33 0^{\circ}) cos (3 0^{\circ}) - cos (33 0^{\circ}) sin (3 0^{\circ})

Rewrite using trig identities:

sin (30 0^{\circ})

= sin (30 0^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

= sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

Use the following trivial identity:

sin (18 0^{\circ}) = 0

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

Use the following trivial identity:

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

= 0 \cdot (- \frac{1}{2}) + (- 1) \frac{3}{2}

Simplify

= - \frac{3}{2}

sin (- \frac{29 π}{6})

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

cos (96 0^{\circ})

sin (arccos (\frac{15}{17}))

arctan (\frac{11}{3})

What is the value of sin(330)cos(30)-cos(330)sin(30) ?
The value of sin(330)cos(30)-cos(330)sin(30) is -(sqrt(3))/2