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

Sagot :

[tex]sin\left(\frac{9\pi}{4}\right)tan\left(\frac{7\pi}{3}\right)=sin\left(2\frac{1}{4}\pi\right)tan\left(2\frac{1}{3}\pi\right)=sin\left(2\pi+\frac{1}{4}\pi\right)tan\left(2\pi+\frac{1}{3}\pi\right)\\\\=sin\frac{1}{4}\pi tan\frac{1}{3}\pi=\frac{\sqrt2}{2}\cdot\sqrt3=\frac{\sqrt6}{2}[/tex]
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