Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Fundamentals of Trigonometric Identities
Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.
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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.
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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:
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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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