Question

Compute without using a calculator.
sin (9π/4)tan(7π/3)

Answer 1

`sin\left((9\pi)/(4)\right)tan\left((7\pi)/(3)\right)=sin\left(2(1)/(4)\pi\right)tan\left(2(1)/(3)\pi\right)=sin\left(2\pi+(1)/(4)\pi\right)tan\left(2\pi+(1)/(3)\pi\right)\\\\=sin(1)/(4)\pi tan(1)/(3)\pi=(\sqrt2)/(2)\cdot\sqrt3=(\sqrt6)/(2)`