What is the value of cos(315)-sin(240)+sin(225) ?

The value of cos(315)-sin(240)+sin(225) is (sqrt(3))/2

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cos(315)-sin(240)+sin(225)

cos (31 5^{\circ}) - sin (24 0^{\circ}) + sin (22 5^{\circ})

\frac{3}{2}

Solution steps

cos (31 5^{\circ}) - sin (24 0^{\circ}) + sin (22 5^{\circ})

Rewrite using trig identities:

sin (24 0^{\circ}) = 2 sin (12 0^{\circ}) cos (12 0^{\circ})

= cos (31 5^{\circ}) - 2 sin (12 0^{\circ}) cos (12 0^{\circ}) + sin (22 5^{\circ})

Rewrite using trig identities:

cos (31 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

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

Use the following trivial identity:

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

Rewrite using trig identities:

sin (22 5^{\circ}) = - \frac{2}{2}

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

Simplify

\frac{2}{2} - 2 \cdot \frac{3}{2} (- \frac{1}{2}) - \frac{2}{2} : \frac{3}{2}

= \frac{3}{2}

3.8 cos (\frac{18 π}{13} - \frac{12 π}{13})

307.58 (cos (2.8))

cot (\frac{4}{5})

arctan (0.56)

arctan (\frac{- 5}{- 4})

What is the value of cos(315)-sin(240)+sin(225) ?
The value of cos(315)-sin(240)+sin(225) is (sqrt(3))/2