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

The value of 4sec((3pi)/4)-4sec(-pi/4) is -8sqrt(2)

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4sec((3pi)/4)-4sec(-pi/4)

4 sec (\frac{3 π}{4}) - 4 sec (- \frac{π}{4})

- 82

Decimal Notation

- 11.31370 \dots

Solution steps

4 sec (\frac{3 π}{4}) - 4 sec (- \frac{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

Rewrite using trig identities:

sec (- \frac{π}{4}) = 2

sec (- \frac{π}{4})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{π}{4}) = sec (\frac{π}{4})

= 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

= 2

= 4 (- 2) - 42

Simplify

= - 82

- 4 cos (6 0^{\circ})

42 cos (3 0^{\circ})

- 10 cos (3 0^{\circ})

arcsin (\frac{3}{3 2})

π (5) (170) (sin (2.8))

What is the value of 4sec((3pi)/4)-4sec(-pi/4) ?
The value of 4sec((3pi)/4)-4sec(-pi/4) is -8sqrt(2)