. Let a be a real number on the interval (-1, 1). A. There are exactly two points on the unit circle of the form (a, y), and there are exactly two points on the unit circle of the form (x, a). Explain. B. Of the two points of the form (a, y) from Part A, the possible values for y are opposites of one another. Of the two points of the (x, a) from Part A, the possible values for a are opposites of one another. Explain. C. If is a real number on the interval [0, 2π] for which a = sin is negative, then could be from exactly two of these four intervals: (0, π/2), (π/2, π), (π, 3π/2), and (3π/2, 2π). Which two are possible, and why?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 52E
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1. Let a be a real number on the interval (–1,1).
A. There are exactly two points on the unit circle of the form (a, y), and there are exactly two points on the unit circle of the form (x, a). Explain.
B. Of the two points of the form (a, y) from Part A, the possible values for y are opposites of one another. Of the two points of the (x, a) from Part A,
the possible values for x are opposites of one another. Explain.
C. If is a real number on the interval [0, 2π] for which a = sin is negative, then could be from exactly two of these four intervals: (0, π/2),
(π/2, π), (π, 3π/2), and (3π/2, 2π). Which two are possible, and why?
Transcribed Image Text:1. Let a be a real number on the interval (–1,1). A. There are exactly two points on the unit circle of the form (a, y), and there are exactly two points on the unit circle of the form (x, a). Explain. B. Of the two points of the form (a, y) from Part A, the possible values for y are opposites of one another. Of the two points of the (x, a) from Part A, the possible values for x are opposites of one another. Explain. C. If is a real number on the interval [0, 2π] for which a = sin is negative, then could be from exactly two of these four intervals: (0, π/2), (π/2, π), (π, 3π/2), and (3π/2, 2π). Which two are possible, and why?
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