Question

how can i work out tan(19pi/4) without a calculator...???

Answer 1

\[\frac{19}{4}=4\tfrac{3}{4}\] and so
\[\frac{19\pi}{4}=2\pi+\frac{3\pi}{4}\]

Answer 2

since tangent is periodic with period pi, you can find this number by finding
\[\tan(\frac{3\pi}{4})\] which if you don't know it amounts to finding
\[\sin(\frac{3\pi}{4})\]
\[\cos(\frac{3\pi}{4})\] and then dividing the first by the second

Answer 3

kinda get that... but then... how do you find sin(3pi/4)....??