What is the value of sin(330) ?

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sin(330)

sin (33 0^{\circ})

- \frac{1}{2}

Solution steps

sin (33 0^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (15 0^{\circ}) + cos (18 0^{\circ}) sin (15 0^{\circ})

= sin (18 0^{\circ}) cos (15 0^{\circ}) + cos (18 0^{\circ}) sin (15 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

Use the following trivial identity:

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

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

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

Simplify

= - \frac{1}{2}

tan (θ) - 1 = 0

sin (θ) = - 1

cos (1)

sin (- 1)

tan (θ) = 2