What is the value of cos(225) ?

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

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cos(225)

cos (22 5^{\circ})

- \frac{2}{2}

Solution steps

cos (22 5^{\circ})

Rewrite using trig identities:

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

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

= - \frac{2}{2}

arctan (\frac{5}{2}) \cdot \frac{180}{π}

cos (3 x) = \frac{1}{2}

tan (3)

2 cos (2 x) + 1 = 0

2 sin^{2} (x) + sin (x) = 1