What is the value of cos((3pi)/4)-sin((3pi)/4) ?

The value of cos((3pi)/4)-sin((3pi)/4) is -sqrt(2)

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cos((3pi)/4)-sin((3pi)/4)

cos (\frac{3 π}{4}) - sin (\frac{3 π}{4})

- 2

Solution steps

cos (\frac{3 π}{4}) - sin (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

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

Simplify

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

= - 2

tan (arcsin (\frac{4}{5}) + arccos (1))

\frac{2 tan ( \frac{7 π}{8} )}{1 - tan ^{2} ( \frac{7 π}{8} )}

sin (11 3^{\circ})

arctan (0.52)

arctan (0.89)

What is the value of cos((3pi)/4)-sin((3pi)/4) ?
The value of cos((3pi)/4)-sin((3pi)/4) is -sqrt(2)