The point P in the figure at the left has y-coordinate
- (a) sin t
- (b) cos t
- (c) tan t
- (d) sec t
(a)
To find: The value for sin t.
Answer to Problem 2T
The value of sin t is
Explanation of Solution
Given:
The value of point y is,
Calculation:
The trigonometric functions of the terminal point on the unit circle is shown as,
Substitute
Since point P lies in quadrant II, therefore sin t is positive.
Hence, the value of sin t is
(b)
To find: The value for cost.
Answer to Problem 2T
The value of cost is
Explanation of Solution
Given:
The value of point y is,
Formula Used:
The equation of unit circle with radius 1 centered at origin is,
Calculation:
The trigonometric functions of the terminal point on the unit circle is shown as,
Use formula of unit circle to find the value of x.
Substitute
Simplify the above equation,
Substitute cost for x in the above equation,
Since point P lies in quadrant II, therefore cost is negative.
Hence, the value of cost is
(c)
To find: The value for tan t.
Answer to Problem 2T
The value of tan t is
Explanation of Solution
Given:
The value of point y is,
Calculation:
The trigonometric functions of the terminal point on the unit circle is shown as,
Substitute
Since point P lies in quadrant II, therefore tan t is negative.
Hence, the value of tan t is
(d)
To find: The value for sec t.
Answer to Problem 2T
The value of sec t is
Explanation of Solution
Given:
The value of point y is,
Calculation:
The trigonometric functions of the terminal point on the unit circle is shown as,
Substitute
Since point P lies in quadrant II, therefore sec t is negative.
Hence, the value of sec t is
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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