What is the value of (cos(0)pi)^1ln(cos(0)pi) ?

The value of (cos(0)pi)^1ln(cos(0)pi) is piln(pi)

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(cos(0)pi)^1ln(cos(0)pi)

(cos (0) π)^{1} ln (cos (0) π)

π ln (π)

Decimal Notation

3.59627 \dots

Solution steps

(cos (0) π)^{1} ln (cos (0) π)

Use the following trivial identity:

cos (0) = 1

cos (0)

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}

= 1

= (1 π)^{1} ln (1 π)

Simplify

= π ln (π)

5 - 5 sin (0)

9 e^{s i n (0)}

2 - 2 sin (0)

2 (\frac{π}{3}) sin (\frac{π}{3}) + cos (\frac{π}{3}) (\frac{π}{3})^{2}

2 (3 0^{\circ}) cos^{2} (3 0^{\circ})

What is the value of (cos(0)pi)^1ln(cos(0)pi) ?
The value of (cos(0)pi)^1ln(cos(0)pi) is piln(pi)