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 (- x - π)

5 sin (- 2 x + 6 0^{\circ}) + 3

sin (arctan (y))

tan (arctan (2 x))

cos (3 t - 6 π)