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To evaluate the six trigonometric functions of ( \frac{3\pi}{4} ), first note that ( \frac{3\pi}{4} ) is located in the second quadrant. The reference angle is ( \frac{\pi}{4} ). The values are:

  • ( \sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2} )
  • ( \cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2} )
  • ( \tan\left(\frac{3\pi}{4}\right) = -1 )
  • ( \csc\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2} ) (reciprocal of sine)
  • ( \sec\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2} ) (reciprocal of cosine)
  • ( \cot\left(\frac{3\pi}{4}\right) = -1 ) (reciprocal of tangent)
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4w ago

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