(a)
The equation and definition of unit circle.
(a)
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)
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)
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)
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)
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 (Standalone Book)
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