Compute without using a calculator:
\(\sin\left(\frac{9\pi}{4}\right) \tan\left(\frac{7\pi}{3}\right)\)
Answer (2)
s in ( 4 9 π ) t an ( 3 7 π ) = s in ( 2 4 1 π ) t an ( 2 3 1 π ) = s in ( 2 π + 4 1 π ) t an ( 2 π + 3 1 π ) = s in 4 1 π t an 3 1 π = 2 2 ⋅ 3 = 2 6
The computation of sin ( 4 9 π ) tan ( 3 7 π ) simplifies to 2 6 after reducing the angles to their equivalent forms. This involves using the periodicity of the sine and tangent functions. The final result can be expressed clearly as 2 6 .
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