Multiple Choice
What is the exact value of ?
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3. Unit Circle
Common Values of Sine, Cosine, & Tangent
Multiple Choice
For which angle is ?
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Verified step by step guidance1
Recall the definition of the cosine function on the unit circle: \(\cos \theta\) represents the x-coordinate of the point on the unit circle at an angle \(\theta\) measured from the positive x-axis.
Understand that \(\cos \theta = -1\) means the point lies on the unit circle where the x-coordinate is -1, which corresponds to the point \((-1, 0)\) on the unit circle.
Identify the angle(s) where the unit circle intersects the point \((-1, 0)\). This occurs at an angle of \(180^\circ\) plus any full rotations of \(360^\circ\), so the general solution is \(\theta = 180^\circ + 360^\circ k\), where \(k\) is any integer.
Check the given angles (\(540^\circ\), \(360^\circ\), \(270^\circ\), \(450^\circ\)) to see which satisfy the equation \(\cos \theta = -1\) by expressing them in terms of \(180^\circ + 360^\circ k\).
Conclude which angle(s) from the given options correspond to \(\cos \theta = -1\) based on the above analysis.
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