What is the value of sec(pi/4)-1/((pi/4)^3)+5 ?

The value of sec(pi/4)-1/((pi/4)^3)+5 is sqrt(2)-(64)/(pi^3)+5

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sec(pi/4)-1/((pi/4)^3)+5

sec (\frac{π}{4}) - \frac{1}{( \frac{π}{4} ) ^{3}} + 5

2 - \frac{64}{π ^{3}} + 5

Decimal Notation

4.35011 \dots

Solution steps

sec (\frac{π}{4}) - \frac{1}{( \frac{π}{4} ) ^{3}} + 5

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

= 2 - \frac{1}{( \frac{π}{4} ) ^{3}} + 5

Simplify

2 - \frac{1}{( \frac{π}{4} ) ^{3}} + 5 : 2 - \frac{64}{π ^{3}} + 5

2 - \frac{1}{( \frac{π}{4} ) ^{3}} + 5

\frac{1}{( \frac{π}{4} ) ^{3}} = \frac{4 ^{3}}{π ^{3}}

\frac{1}{( \frac{π}{4} ) ^{3}}

(\frac{π}{4})^{3} = \frac{π ^{3}}{4 ^{3}}

(\frac{π}{4})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{π ^{3}}{4 ^{3}}

= \frac{1}{\frac{π ^{3}}{4 ^{3}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{4 ^{3}}{π ^{3}}

= 2 - \frac{4 ^{3}}{π ^{3}} + 5

4^{3} = 64

= 2 - \frac{64}{π ^{3}} + 5

= 2 - \frac{64}{π ^{3}} + 5

tan (- \frac{17 π}{4})

sec^{2} (2 (\frac{π}{6})) \cdot 2

cos (\frac{7 π}{10})

\frac{39}{sin ( 3 2 ^{\circ} )}

8 cos (9 0^{\circ})

What is the value of sec(pi/4)-1/((pi/4)^3)+5 ?
The value of sec(pi/4)-1/((pi/4)^3)+5 is sqrt(2)-(64)/(pi^3)+5