How do I find the value of sec -3pi/4?

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How do I find the value of sec -3pi/4?

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Answer 1 · 2015-08-22T12:52:22

$sec (\frac{- 3 π}{4}) = - \sqrt{2}$ $sec((-3pi)/4) = -sqrt(2)$

Explanation:

$sec = \frac{hypothenuse}{adjacent side}$ $sec = ("hypothenuse")/("adjacent side")$
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Answer 2 · 2015-08-22T23:39:09

Find $sec (\frac{- 3 π}{4})$ $sec ((-3pi)/4)$

Ans: $- \sqrt{2}$ $- sqrt2$

Explanation:

Another way to find $sec (\frac{- 3 π}{4})$ $sec((-3pi)/4)$

$sec (\frac{- 3 π}{4}) = \frac{1}{sin (\frac{- 3 π}{4})} .$ $sec ((-3pi)/4) = 1/sin ((-3pi)/4).$ Find $sin (\frac{- 3 π}{4})$ $sin ((-3pi)/4)$

On the trig unit circle,
$sin (\frac{- 3 π}{4}) = sin (- \frac{π}{4}) = - sin (\frac{π}{4}) = - \frac{\sqrt{2}}{2}$ $sin ((-3pi)/4) = sin (-pi/4) = - sin (pi/4) = - sqrt2/2$
Therefor:
$sec (\frac{- 3 π}{4}) = (\frac{1}{sin}) = - \frac{2}{\sqrt{2}} = - \sqrt{2}$ $sec ((-3pi)/4) = (1/sin) = -2/sqrt2 = - sqrt2$

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How do I find the value of sec -3pi/4?

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