객관식
Consider the equation . If is an angle in Quadrant II, what is the value of ?
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3. Unit Circle
Trigonometric Functions on the Unit Circle
Multiple Choice
On the unit circle, for , when is undefined?
A
When
B
When
C
When
D
When
검증된 단계별 안내1
Recall that on the unit circle, the tangent of an angle \( \theta \) is defined as the ratio of the sine to the cosine:
\[ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \]
Understand that tangent is undefined when the denominator of this ratio, \( \cos(\theta) \), is zero because division by zero is undefined.
Identify the values of \( \theta \) between 0 and \( \pi \) where \( \cos(\theta) = 0 \). On the unit circle, \( \cos(\theta) = 0 \) at \( \theta = \frac{\pi}{2} \).
Note that at \( \theta = \pi \), \( \cos(\pi) = -1 \), which is not zero, so tangent is defined there.
Conclude that within the interval \( 0 < \theta < \pi \), \( \tan(\theta) \) is undefined only when \( \theta = \frac{\pi}{2} \).
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