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(a)
The equation and definition of unit circle.
(a)
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Explanation of Solution
A unit circle is a circle with radius one unit whose centre lies on the origin
The equation of a unit circle is shown below.
Therefore, a unit circle is a circle with radius 1 unit whose equation is
(b)
To explain: The term terminal point determined by t with the help of a diagram.
(b)
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Explanation of Solution
Consider a unit circle with the starting point
Consider a point
Figure (1)
It is clearly seen from the above figure that the terminal point is
Therefore, the term used for the end point after covering t distance in counterclockwise direction of a unit circle is terminal point.
(c)
The terminal point for
(c)
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Answer to Problem 1RCC
The terminal point determined by
Explanation of Solution
Consider a unit circle with the starting point
Figure (2)
Therefore, the terminal point determined by
(d)
To explain: The reference point associated with t.
(d)
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Explanation of Solution
Let t is a real number.
The reference number
To obtain the reference, it is very important to know the position of t in the quadrant.
If the terminal point lies on first or fourth quadrant, where x is positive then
Thus, the reference number
(e)
The reference number and terminal point for
(e)
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Answer to Problem 1RCC
The reference number for
Explanation of Solution
The reference point
The reference number for
The reference number is
Since the terminal point determined by t is in fourth quadrant therefore, x coordinate is positive and y coordinate is negative.
Hence the terminal point is
Thus, the reference number for
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Chapter 5 Solutions
Precalculus: Mathematics for Calculus
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