What is the value of log_{2}(sec(pi/4)) ?

The value of log_{2}(sec(pi/4)) is 1/2

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log_{2}(sec(pi/4))

lo g_{2} (sec (\frac{π}{4}))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

lo g_{2} (sec (\frac{π}{4}))

Use the following trivial identity:

sec (\frac{π}{4}) = 2

sec (\frac{π}{4})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

= lo g_{2} (2)

Simplify

lo g_{2} (2) : \frac{1}{2}

lo g_{2} (2)

Rewrite as

= lo g_{2} (2^{\frac{1}{2}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{2} lo g_{2} (2)

Apply log rule:

lo g_{a} (a) = 1

= \frac{1}{2}

= \frac{1}{2}

sin (20 0^{\circ}) cos (8 0^{\circ}) - cos (20 0^{\circ}) sin (8 0^{\circ})

arcsin (\frac{1}{1.52})

\frac{2}{π \cdot 0.1} tan (\frac{π \cdot 0.1}{2})

1 - 2 sin^{2} (\frac{2 π}{9})

- 2 cos (12 0^{\circ})

What is the value of log_{2}(sec(pi/4)) ?
The value of log_{2}(sec(pi/4)) is 1/2