What is the value of 16sin((2pi)/4) ?

The value of 16sin((2pi)/4) is 16

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16sin((2pi)/4)

16 sin (\frac{2 π}{4})

16

Solution steps

16 sin (\frac{2 π}{4})

Rewrite using trig identities:

sin (\frac{2 π}{4}) = 1

sin (\frac{2 π}{4})

Simplify:

\frac{2 π}{4} = \frac{π}{2}

\frac{2 π}{4}

Cancel the common factor:

2

= \frac{π}{2}

= sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1

= 16 \cdot 1

Simplify

= 16

arccos (\frac{17}{20})

arccos (- \frac{8}{14 \cdot 61})

arctan (\frac{50 3}{π})

2 e^{3 s i n (2)} + e^{2}

25 π cos (\frac{π \frac{1}{2}}{2})