What is the value of sin((5pi)/4)+cos((5pi)/4) ?

The value of sin((5pi)/4)+cos((5pi)/4) is -sqrt(2)

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sin((5pi)/4)+cos((5pi)/4)

sin (\frac{5 π}{4}) + cos (\frac{5 π}{4})

- 2

Solution steps

sin (\frac{5 π}{4}) + cos (\frac{5 π}{4})

Rewrite using trig identities:

sin (\frac{5 π}{4}) = - \frac{2}{2}

Rewrite using trig identities:

cos (\frac{5 π}{4}) = - \frac{2}{2}

= - \frac{2}{2} - \frac{2}{2}

Simplify

- \frac{2}{2} - \frac{2}{2} : - 2

= - 2

tan (- \frac{11 π}{4})

arccos (\frac{3}{13})

arctan (\frac{300}{400})

cos (\frac{π}{12}) + i sin (\frac{π}{12})

sin (\frac{11}{6} π)

What is the value of sin((5pi)/4)+cos((5pi)/4) ?
The value of sin((5pi)/4)+cos((5pi)/4) is -sqrt(2)