What is cos(x-(5pi)/4) ?

The solution to cos(x-(5pi)/4) is -sin(pi/4+x)

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simplify cos(x-(5pi)/4)

simplify

cos (x - \frac{5 π}{4})

- sin (\frac{π}{4} + x)

Solution steps

cos (x - \frac{5 π}{4})

Rewrite using trig identities

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

sin^{2} (θ) - 1 + 2 cos (θ) sin (θ)

1 - sin^{2} (- x)

sin (- y) - sin (2 π - y)

49 tan^{2} (x) + 49

- sin (27 0^{\circ} - x)