M:N:MC:15
Exam
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Skill
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It is given that where x is the radian measure of an angle and
If which of the following could be the value of w?
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Choice B is correct. If an angle with radian measure x such that is placed in standard position, its terminal side will fall in Quadrant II, and
will be the y-coordinate of the point P where its terminal side intersects the unit circle. If
then when the angle with radian measure w is placed in standard position, its terminal side will intersect the unit circle at a point with y-coordinate equal to
There are two such points on the unit circle: the reflection of P across the x-axis, which would correspond to an angle with radian measure –x (and also with radian measures...
and the reflection of P through the origin, which would correspond to an angle with radian measure
(and also with radian measures ...
Thus, of the choices given, only
could be the value of w.
Choice A is not the correct answer. In general, and
so
Therefore,
not
Choice C is not the correct answer. In general, so
, not
Choice D is not the correct answer. In general, so
not
Students must be fluent with radian measure and have a conceptual understanding of trigonometric relationships.