What is the value of tan((pi/2)/2) ?

The value of tan((pi/2)/2) is 1

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tan((pi/2)/2)

tan (\frac{\frac{π}{2}}{2})

1

Solution steps

tan (\frac{\frac{π}{2}}{2})

Simplify:

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

= tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 1

2 - 2 sin (\frac{7 π}{6})

arcsin (\frac{1}{2.5})

\frac{1 + cos ( \frac{7 π}{6} )}{sin ( \frac{7 π}{6} )}

- \frac{cos ( π )}{2}

sin (0.93)