What is the value of 6sec^2(2(pi/2)) ?

The value of 6sec^2(2(pi/2)) is 6

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6sec^2(2(pi/2))

6 sec^{2} (2 (\frac{π}{2}))

6

Solution steps

6 sec^{2} (2 (\frac{π}{2}))

= 6 sec^{2} (2 \cdot \frac{π}{2})

Rewrite using trig identities:

sec (2 \cdot \frac{π}{2}) = - 1

sec (2 \cdot \frac{π}{2})

Simplify:

2 \cdot \frac{π}{2} = π

2 \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 2}{2}

Cancel the common factor:

2

= π

= sec (π)

Use the following trivial identity:

sec (π) = (- 1)

sec (π)

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}

= (- 1)

= - 1

= 6 (- 1)^{2}

Simplify

6 (- 1)^{2} : 6

6 (- 1)^{2}

(- 1)^{2} = 1

(- 1)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 1)^{2} = 1^{2}

= 1^{2}

Apply rule

1^{a} = 1

= 1

= 6 \cdot 1

Multiply the numbers:

6 \cdot 1 = 6

= 6

= 6

100 (cos (\frac{1}{5}) - cos (\frac{1}{10}))

e^{s i n (i)}

ln (cos (\frac{π}{6}))

\frac{sin ( 4 5 ^{\circ} )}{2}

\frac{119}{sin ( 2.8 )}