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

The value of 2sec((3pi)/4) is -2sqrt(2)

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2sec((3pi)/4)

2 sec (\frac{3 π}{4})

- 22

Decimal Notation

- 2.82842 \dots

Solution steps

2 sec (\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

= 2 (- 2)

Simplify

= - 22

sec^{2} (2 - 2)

arctan (cos (3 π))

π cos (π \cdot 1)

arccos (cos (- π))

sin (4 \frac{4 π}{3})