What is sin(x-pi/4) ?

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

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simplify sin(x-pi/4)

simplify

sin (x - \frac{π}{4})

sin (- \frac{π}{4} + x)

Solution steps

sin (x - \frac{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)

Could not simplify further

= sin (- \frac{π}{4} + x)

sin (\frac{π}{2} - θ) sec (θ)

\frac{x ln ( x )}{cos ( x )}

- cos (18 0^{\circ} + a) + cos (a)

cos (4 t - π) - sin (4 t - π)

csc (- x^{0})