What is sin(x-(3pi)/4) ?

The solution to sin(x-(3pi)/4) is -sin(pi/4+x)

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simplify sin(x-(3pi)/4)

simplify

sin (x - \frac{3 π}{4})

- sin (\frac{π}{4} + x)

Solution steps

sin (x - \frac{3 π}{4})

Rewrite using trig identities

= \frac{- 2 sin ( x ) - 2 cos ( x )}{2}

Factor

- cos (x) 2 - sin (x) 2 : - 2 (cos (x) + sin (x))

= \frac{- ( cos ( x ) + sin ( x ) ) 2}{2}

Rewrite using trig identities

= - sin (\frac{π}{4} + x)

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

- sin (2 x - 5 x)

cos (x + 18 0^{\circ})

cos (\frac{π}{6} + t)

sin (2 t - 2 π)