What is the value of cos((pi^1)/2) pi/2 ?

The value of cos((pi^1)/2) pi/2 is 0

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cos((pi^1)/2) pi/2

cos (\frac{π ^{1}}{2}) \frac{π}{2}

0

Solution steps

cos (\frac{π ^{1}}{2}) \frac{π}{2}

Simplify:

\frac{π ^{1}}{2} = \frac{π}{2}

\frac{π ^{1}}{2}

Apply rule

a^{1} = a

π^{1} = π

= \frac{π}{2}

cos (\frac{π}{2}) \frac{π}{2} = \frac{π cos ( \frac{π}{2} )}{2}

cos (\frac{π}{2}) \frac{π}{2}

Multiply fractions:

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

= \frac{π cos ( \frac{π}{2} )}{2}

= \frac{π cos ( \frac{π}{2} )}{2}

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= \frac{π 0}{2}

Simplify

= 0

tan (\frac{11 π}{6} - \frac{5 π}{4})

8 \cdot sin (5 0^{\circ})

2 sin (5 0^{\circ})

2 sin (2 5^{\circ}) cos (2 5^{\circ})

arcsin (- 7)