What is the value of 40*sec^2(((20pi)/3)/(40))*1/40*355 ?

The value of 40*sec^2(((20pi)/3)/(40))*1/40*355 is 1420/3

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40sec^2(((20pi)/3)/(40))1/40*355

40 \cdot sec^{2} (\frac{\frac{20 π}{3}}{40}) \cdot \frac{1}{40} \cdot 355

\frac{1420}{3}

Solution steps

40 sec^{2} (\frac{\frac{20 π}{3}}{40}) \frac{1}{40} \cdot 355

Simplify:

\frac{\frac{20 π}{3}}{40} = \frac{π}{6}

40 sec^{2} (\frac{π}{6}) \frac{1}{40} \cdot 355 = 355 sec^{2} (\frac{π}{6})

= 355 sec^{2} (\frac{π}{6})

Use the following trivial identity:

sec (\frac{π}{6}) = \frac{2 3}{3}

= 355 (\frac{2 3}{3})^{2}

Simplify

355 (\frac{2 3}{3})^{2} : \frac{1420}{3}

= \frac{1420}{3}

3 (cos (\frac{π}{6}) + i sin (\frac{π}{6}))

arctan (0.07)

arctan (0.11)

arctan (\frac{100}{1500})

240 sin (2 5^{\circ})

What is the value of 40*sec^2(((20pi)/3)/(40))*1/40*355 ?
The value of 40*sec^2(((20pi)/3)/(40))*1/40*355 is 1420/3