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Popular >

ln|sin(pi/2)|

Solution

ln sin (\frac{π}{2})

Solution

0

Solution steps

ln 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

= ln ∣ 1 ∣

Simplify

ln ∣ 1 ∣ : 0

ln ∣ 1 ∣

Simplify

∣ 1 ∣ : 1

∣ 1 ∣

Apply absolute rule:

∣ a ∣ = a, a \geq 0

∣ 1 ∣ = 1

= 1

= ln (1)

Apply log rule:

lo g_{a} (1) = 0

= 0

= 0

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Frequently Asked Questions (FAQ)

What is the value of ln|sin(pi/2)| ?
The value of ln|sin(pi/2)| is 0