What is the value of sin(225) ?

The value of sin(225) is -(sqrt(2))/2

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sin(225)

sin (22 5^{\circ})

- \frac{2}{2}

Solution steps

sin (22 5^{\circ})

Rewrite using trig identities:

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

= sin (18 0^{\circ}) cos (4 5^{\circ}) + cos (18 0^{\circ}) sin (4 5^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

= - \frac{2}{2}

2 cos^{2} (θ) - 1 = 0

2 tan^{2} (30 0^{\circ}) + 3 sin^{2} (15 0^{\circ}) - cos^{2} (18 0^{\circ})

cos (2 x) = - \frac{3}{2}, - π \leq x \leq \frac{π}{2}

cos (2 θ) = cos^{2} (θ) - \frac{1}{2}

arccos (cos (\frac{7 π}{6}))