What is the value of sin(15) ?

The value of sin(15) is (sqrt(6)-sqrt(2))/4

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sin(15)

sin (1 5^{\circ})

\frac{6 - 2}{4}

Solution steps

sin (1 5^{\circ})

Rewrite using trig identities:

sin (4 5^{\circ}) cos (3 0^{\circ}) - cos (4 5^{\circ}) sin (3 0^{\circ})

= sin (4 5^{\circ}) cos (3 0^{\circ}) - cos (4 5^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

= \frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2}

Simplify

\frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2} : \frac{6 - 2}{4}

= \frac{6 - 2}{4}

sec (- \frac{π}{4})

sec (- \frac{π}{3})

sin^{2} (3 0^{\circ})

cos (- \frac{4 π}{3})

sec (x) = 2