What is cos(t+pi/4) ?

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

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simplify cos(t+pi/4)

simplify

cos (t + \frac{π}{4})

- sin (- \frac{π}{4} + t)

Solution steps

cos (t + \frac{π}{4})

Rewrite using trig identities

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

Rewrite using trig identities

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

Factor

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

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

Express with sin, cos

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

Rewrite using trig identities

= - sin (- \frac{π}{4} + t)

sin (arccos (t))

4 - (2 sin (x))^{2}

cot (\frac{π}{2} + x)

cos (arcsin (19 x))

tan (36 0^{\circ} + x)