What is the value of sec((-7pi)/4) ?

The value of sec((-7pi)/4) is square root of 2

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sec((-7pi)/4)

sec (\frac{- 7 π}{4})

2

Solution steps

sec (\frac{- 7 π}{4})

Simplify

= sec (- \frac{7 π}{4})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{7 π}{4}) = sec (\frac{7 π}{4})

= sec (\frac{7 π}{4})

Rewrite using trig identities:

\frac{1}{cos ( \frac{7 π}{4} )}

= \frac{1}{cos ( \frac{7 π}{4} )}

Rewrite using trig identities:

cos (\frac{7 π}{4}) = \frac{2}{2}

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

Simplify

\frac{1}{\frac{2}{2}} : 2

= 2

sin (3 0^{\circ}) cos (6 0^{\circ})

\frac{6.6}{sin ( 2 9 ^{\circ} )}

\frac{24}{sin ( 4 6 ^{\circ} )}

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

cos (arcsin (- 1))

What is the value of sec((-7pi)/4) ?
The value of sec((-7pi)/4) is square root of 2