What is the value of 3sec^2((3pi)/4) ?

The value of 3sec^2((3pi)/4) is 6

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3sec^2((3pi)/4)

3 sec^{2} (\frac{3 π}{4})

6

Solution steps

3 sec^{2} (\frac{3 π}{4})

Use the following trivial identity:

sec (\frac{3 π}{4}) = - 2

sec (\frac{3 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

= 3 (- 2)^{2}

Simplify

3 (- 2)^{2} : 6

3 (- 2)^{2}

(- 2)^{2} = 2

(- 2)^{2}

Apply exponent rule:

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

n

is even

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

= (2)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

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

= 2^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

= 6

2 sin (\frac{2 π}{5}) cos (\frac{2 π}{5})

\frac{sin ( 84 0 ^{\circ} )}{cos ( 33 0 ^{\circ} ) + sin ( 31 5 ^{\circ} )}

cos (arctan (3) + arcsin (\frac{1}{3}))

tan (\frac{5 π}{6} - \frac{5 π}{4})

sin (arcsec (8))