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}

Rewrite using trig identities

= \frac{1 - tan ( x )}{sec ( x ) 2}

Factor

\frac{1 - tan ( x )}{sec ( x ) 2} : \frac{- 2 ( tan ( x ) - 1 )}{2 sec ( x )}

= \frac{- ( - 1 + tan ( x ) ) 2}{2 sec ( x )}

Express with sin, cos

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

Rewrite using trig identities

= - sin (- \frac{π}{4} + x)

\frac{1}{cos ^{2} ( x )} d x

cos (x + \frac{π}{6})

tan (arcsin (\frac{4}{x}))

\frac{1}{1 + tan ^{2} ( θ )}

sin (x + \frac{2 π}{3})