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

The value of -cos((5pi)/4)-sin((5pi)/4) is square root of 2

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

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

2

Solution steps

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

Rewrite using trig identities:

cos (\frac{5 π}{4}) = - \frac{2}{2}

Rewrite using trig identities:

sin (\frac{5 π}{4}) = - \frac{2}{2}

= - (- \frac{2}{2}) - (- \frac{2}{2})

Simplify

- (- \frac{2}{2}) - (- \frac{2}{2}) : 2

= 2

4 sin (37. 5^{\circ}) cos (7.5)

cos (2 \cdot 30)

arcsin (\frac{32}{35})

4 cos^{2} (\frac{π}{2})

- sec (- \frac{π}{2})

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