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

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

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

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

- \frac{3}{2}

Solution steps

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

Rewrite using trig identities:

sin (24 0^{\circ}) = - \frac{3}{2}

Rewrite using trig identities:

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

Rewrite using trig identities:

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

= - \frac{3}{2} - \frac{2}{2} + \frac{2}{2}

Simplify

- \frac{3}{2} - \frac{2}{2} + \frac{2}{2} : - \frac{3}{2}

= - \frac{3}{2}

12 sin (9 0^{\circ})

\frac{12 sin ( 12. 9 ^{\circ} )}{sin ( 10 0 ^{\circ} )}

tan^{2} (12 1^{\circ})

tan^{2} (6 3^{\circ}) - sec^{2} (6 3^{\circ})

4 tan (6 0^{\circ})

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