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

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

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

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

- 2

Solution steps

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

Rewrite using trig identities:

sin (\frac{5 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

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

= - 2

\frac{7}{tan ( 4 6 ^{\circ} )}

\frac{0}{sin ^{2} ( 0 )}

sin (2 arcsin (- \frac{1}{3}))

sin (\frac{π}{3}) - cos (\frac{π}{3})

cos^{2} (1) - e^{- 2}

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