(3/2, 3/2 1. The point centered at the origin. a. What is the radius of the circle? Show lies on a circle your work. b. What is the equation of the circle? c. Draw the reference triangle for the angle O which has terminal side intersecting the circle in this point, labeling the side lengths. d. Find the values of the six trigonometric functions for 0. e. What is 0? Express it in both degrees and radians, and explain how you know f. Find all of the angles within l-27, 27, which have the same cotangent as 0. Illustrate on the circle. What are the angles in degrees?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 79E
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The point(3√2, 3√2) lies on a circle centered at the origin.

  1. Find the values of the six trigonometric functions for theta .
  2. What is theta? Express it in both degrees and radians, and explain how you know.
  3. Find all of the angles within [-2pi, 2pi] which have the same cotangent as theta . Illustrate on the circle. What are the angles in degrees?

 

One attached picture is the full question and the other picture is the work for the first 3 problems of those questions.

part-1-of-week-2-individual-wr...
(3v2, 3v2
1. The point
centered at the origin.
a. What is the radius of the circle? Show
lies on a circle
your work.
b. What is the equation of the circle?
c. Draw the reference triangle for the
angle O which has terminal side
intersecting the circle in this point,
labeling the side lengths.
d. Find the values of the six trigonometric
functions for 0.
e. What is 0? Express it in both degrees
and radians, and explain how you know.
f. Find all of the angles within l-27, 2)
which have the same cotangent as U.
|
Illustrate on the circle. What are the
angles in degrees?
-3/5 and
2. An angle 0 has cos 0 =
tan 0 > 0.
a. What Quadrant is O in?
b. What are the coordinates of the point
where the terminal side of 0 intersects
the unit circle? Show your work and
draw the point on the unit circle.
c. Find the values of the remaining
trigonometric functions of . Show all
work.
Transcribed Image Text:part-1-of-week-2-individual-wr... (3v2, 3v2 1. The point centered at the origin. a. What is the radius of the circle? Show lies on a circle your work. b. What is the equation of the circle? c. Draw the reference triangle for the angle O which has terminal side intersecting the circle in this point, labeling the side lengths. d. Find the values of the six trigonometric functions for 0. e. What is 0? Express it in both degrees and radians, and explain how you know. f. Find all of the angles within l-27, 2) which have the same cotangent as U. | Illustrate on the circle. What are the angles in degrees? -3/5 and 2. An angle 0 has cos 0 = tan 0 > 0. a. What Quadrant is O in? b. What are the coordinates of the point where the terminal side of 0 intersects the unit circle? Show your work and draw the point on the unit circle. c. Find the values of the remaining trigonometric functions of . Show all work.
Solution 1: The radius r equals the length
between (0, 0) and (3 – V2,3 – V2). Therefore,
-
-
(3 – V2- 0)° + (3 – VI - 0)*
(3 – V2) + (3 – v2)*
r =
r =
-
-
= V2(3 – V2)
= v² (3 – V2)
3/2 – 2
r =
r =
r =
Solution 2: The equation of the circle with a
radius r = 3/2 – 2 and centered at (0,0) is
:3V
(x – 0)² + (v – 0)² = (3 /2 – 2)
x? + y? =18 + 4 – 12/2
x² + y²=22 – 12 v2
Solution 3:
Transcribed Image Text:Solution 1: The radius r equals the length between (0, 0) and (3 – V2,3 – V2). Therefore, - - (3 – V2- 0)° + (3 – VI - 0)* (3 – V2) + (3 – v2)* r = r = - - = V2(3 – V2) = v² (3 – V2) 3/2 – 2 r = r = r = Solution 2: The equation of the circle with a radius r = 3/2 – 2 and centered at (0,0) is :3V (x – 0)² + (v – 0)² = (3 /2 – 2) x? + y? =18 + 4 – 12/2 x² + y²=22 – 12 v2 Solution 3:
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