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Calculus Level 2

What is 16tan^2(pi/3)sin^4(pi/4)?


The answer is 12.

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2 solutions

Ikkyu San
May 19, 2015

From tan π 3 = 3 \color{#D61F06}{\tan{\dfrac{\pi}{3}}=\sqrt{3}} and sin π 4 = 1 2 \color{#3D99F6}{\sin{\dfrac{\pi}{4}}=\dfrac{1}{\sqrt{2}}}

Thus,

16 tan 2 π 3 sin 4 π 4 = 16 ( 3 ) 2 ( 1 2 ) 4 = 16 ( 3 ) ( 1 4 ) = 4 ( 3 ) = 12 \begin{aligned}16\color{#D61F06}{\tan}^2{\color{#D61F06}{\dfrac{\pi}{3}}}\color{#3D99F6}{\sin}^4{\color{#3D99F6}{\dfrac{\pi}{4}}}=&\ 16(\color{#D61F06}{\sqrt{3}})^2\left(\color{#3D99F6}{\dfrac{1}{\sqrt{2}}}\right)^4\\=&\ 16(3)\left(\dfrac{1}{4}\right)\\=&\ 4(3)=\boxed{12}\end{aligned}

Hemant Mathur
May 18, 2015

16 tan^2 (pi/3) sin^4(pi/4) = (48)/4 =12

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