Explanation Given information: The unit circle is Explanation: Let P ( x , y ) be the point on the unit circle that corresponds to the angle θ . By using definition of trigonometric functions, sin θ = y , cos θ = x . The angle π 3 and the angle B lies on the same line. The measure of an angle B from the x − axis is π 3 + π = 4 π 3 Since the angle between the π 3 and the B is π ; therefore, the measure of the angle B is 4 π 3 Similarly, The angle π 4 and the angle C lie on the same line. The measure of an angle C from the x − axis is π 4 + π = 5 π 4 Therefore, the measure of an angle C is 5 π 4 . The angle π 6 and the angle D lie on the same line. The measure of an angle D from the x − axis is π 6 + π = 7 π 6 Therefore, the measure of an angle D is 7 π 6 The angle 0 and the angle E lie on the same line. The measure of an angle E from the x − axis is 0 + π = π Therefore, the measure of an angle E is π . The angle 11 π 6 and the angle F lie on the same line. The measure of an angle F from the x − axis is 11 π 6 − π = 5 π 6 Therefore, the measure of an angle F is 5 π 6 The angle 7 π 4 and the angle G lie on the same line. The measure of an angle G from the x − axis is 7 π 4 − π = 3 π 4 Therefore, the measure of an angle G is 3 π 4 . The angle 5 π 3 and the angle H lie on the same line. The measure of an angle H from the x − axis is 5 π 3 − π = 2 π 3 Therefore, the measure of an angle H is 2 π 3 The measure of angle I is π 2 The angle A and the angle I lie on the same line. The measure of an angle A from the x − axis is π 2 + π = 3 π 2 Therefore, the measure of an angle A is 3 π 2 i) When θ = 0 , sin 0 = 0 , cos 0 = 1 Thus, the point P is ( 1 , 0 ) Therefore, the point corresponding to the angle 0 is ( 1 , 0 ) ii) When θ = π 6 , sin π 6 = 1 2 , cos π 6 = 3 2 Thus, the point P is ( 3 2 , 1 2 ) Therefore, the point corresponding to the angle π 6 is ( 3 2 , 1 2 ) iii) When θ = π 4 , sin π 4 = 2 2 , cos π 4 = 2 2 Thus, the point P is ( 2 2 , 2 2 ) Therefore, the point corresponding to the angle π 4 is ( 2 2 , 2 2 ) iv)When θ = π 3

11th Edition

ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 6, Problem 55RE

To determine

To fill: The missing angles and the corresponding points P on the given unit circle,

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 54RE

Chapter 6, Problem 1CT

Students have asked these similar questions

4. Please solve this for me and show every single step. I am studying and got stuck on this practice question, and need help in solving it. Please be very specific and show every step. Thanks. I WANT A HUMAN TO SOLVE THIS PLEASE.

3. Please solve this for me and show every single step. I am studying and got stuck on this practice question, and need help in solving it. Please be very specific and show every step. Thanks.

5. Please solve this for me and show every single step. I am studying and got stuck on this practice question, and need help in solving it. Please be very specific and show every step. Thanks. I WANT A HUMAN TO SOLVE THIS PLEASE.

Chapter 6 Solutions

Precalculus

Ch. 6.1 - What is the formula for the circumference C of a...Ch. 6.1 - If an object has a speed of r feet per second and...Ch. 6.1 - An angle is in _____ _____ if its vertex is at...Ch. 6.1 - A _____ _____ is a positive angle whose vertex is...Ch. 6.1 - If the radius of a circle is r and the length of...Ch. 6.1 - On a circle of radius r , a central angle of ...Ch. 6.1 - 180 = _____ radians a. 2 b. c. 3 2 d. 2 Ch. 6.1 - An object travels on a circle of radius r with...Ch. 6.1 - True or False The angular speed of an object...Ch. 6.1 - True or False For circular motion on a circle of...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The missing angles and the corresponding points P on the given unit circle,

Solution Summary: The author explains how to fill in the missing angles and corresponding points P on the given unit circle.

Videos

To fill: The missing angles and the corresponding points P on the given unit circle,

Want to see the full answer?

Chapter 6 Solutions