Find the trigonometric values for an angle in the unit circle
Answer 1
Henry Green
Given an angle \( \theta = \frac{5\pi}{4} \), find the values of \( \sin(\theta) \), \( \cos(\theta) \), and \( \tan(\theta) \).
First, determine the reference angle in the unit circle. \( \theta = \frac{5\pi}{4} \) is in the third quadrant. The reference angle is \( \pi + \frac{\pi}{4} = \frac{5\pi}{4} \).
For the angle \( \frac{5\pi}{4} \):
\( \sin(\frac{5\pi}{4}) = -\frac{\sqrt{2}}{2} \)
\( \cos(\frac{5\pi}{4}) = -\frac{\sqrt{2}}{2} \)
\( \tan(\frac{5\pi}{4}) = 1 \)
Therefore, the values are:
\( \sin(\frac{5\pi}{4}) = -\frac{\sqrt{2}}{2} \)
\( \cos(\frac{5\pi}{4}) = -\frac{\sqrt{2}}{2} \)
\( \tan(\frac{5\pi}{4}) = 1 \)
Answer 2
Alex Thompson
Given ( heta = frac{5pi}{4} ), we need to find ( sin( heta) ), ( cos( heta) ), and ( an( heta) ).
Since ( heta ) is in the third quadrant:
( sin( heta) = -sin(frac{pi}{4}) = -frac{sqrt{2}}{2} )
( cos( heta) = -cos(frac{pi}{4}) = -frac{sqrt{2}}{2} )
( an( heta) = frac{sin( heta)}{cos( heta)} = frac{-frac{sqrt{2}}{2}}{-frac{sqrt{2}}{2}} = 1 )
Thus, the values are:
( sin(frac{5pi}{4}) = -frac{sqrt{2}}{2} )
( cos(frac{5pi}{4}) = -frac{sqrt{2}}{2} )
( an(frac{5pi}{4}) = 1 )
Answer 3
Ella Lewis
Given ( heta = frac{5pi}{4} ):
( sin( heta) = -frac{sqrt{2}}{2} )
( cos( heta) = -frac{sqrt{2}}{2} )
( an( heta) = 1 )
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