Multiple Choice
Evaluate each expression.
3. Unit Circle
Reciprocal Trigonometric Functions on the Unit Circle
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Evaluate each expression.
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Verified step by step guidance1
Understand that the cosecant function, \( \csc \theta \), is the reciprocal of the sine function, \( \sin \theta \). Therefore, \( \csc 225^\circ = \frac{1}{\sin 225^\circ} \).
Recognize that 225° is in the third quadrant of the unit circle, where both sine and cosine are negative.
Recall that the reference angle for 225° is 45°, since 225° - 180° = 45°.
Use the fact that \( \sin 45^\circ = \frac{\sqrt{2}}{2} \). Since 225° is in the third quadrant, \( \sin 225^\circ = -\frac{\sqrt{2}}{2} \).
Calculate \( \csc 225^\circ = \frac{1}{\sin 225^\circ} = \frac{1}{-\frac{\sqrt{2}}{2}} = -\sqrt{2} \).
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