Trigonometry (11th Edition) 11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
1 Trigonometric Functions 2 Acute Angles And Right Triangles 3 Radian Measure And The Unit Circle 4 Graphs Of The Circular Functions 5 Trigonometric Identities 6 Inverse Circular Functions And Trigonometric Equations 7 Applications Of Trigonometry And Vectors 8 Complex Numbers, Polar Equations, And Parametric Equations A Equations And Inequalities B Graphs Of Equations C Functions D Graphing Techniques Chapter1: Trigonometric Functions
1.1 Angles 1.2 Angle Relationships And Similar Triangles 1.3 Trigonometric Functions 1.4 Using The Definitions Of The Trigonometric Functions Chapter Questions Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Problem 2RE: Find the angle of least positive measure that is coterminal with each angle. 51 Problem 3RE:
Find the angle of least positive measure that is coterminal with each angle.
3. –174°
Problem 4RE: Find the angle of least positive measure that is coterminal with each angle. 792 Problem 5RE: Rotating Propeller The propeller of a speedboat rotates 650 times per min. Through how many degrees... Problem 6RE:
6. Rotating Pulley A pulley is rotating 320 times per min. Through how many degrees does a point on... Problem 7RE: Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to... Problem 8RE:
Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to... Problem 9RE:
Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to... Problem 10RE: Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to... Problem 11RE:
Find the measure of each marked angle.
11.
Problem 12RE: Find the measure of each marked angle. Problem 13RE Problem 14RE Problem 15RE: Length of a Road A camera is located on a satellite with its lens positioned at C in the figure.... Problem 16RE:
16. Express θ in terms of α and β
Problem 17RE: Find all unknown angle measures in each pair of similar triangles. Problem 18RE: Find all unknown angle measures in each pair of similar triangles. Problem 19RE:
Find the unknown side lengths in each pair of similar triangles.
19.
Problem 20RE Problem 21RE Problem 22RE Problem 23RE:
23. Length of a Shadow If a tree 20 ft tall casts a shadow 8 ft long, how long would the shadow of... Problem 24RE: Find the six trigonometric function values for each angle. Rationalize denominators when applicable. Problem 25RE Problem 26RE: Find the six trigonometric function values for each angle. Rationalize denominators when applicable. Problem 27RE Problem 28RE: Find the values of the six trigonometric functions for an angle in standard position having each... Problem 29RE Problem 30RE Problem 31RE Problem 32RE Problem 33RE: An equation of the terminal side of an angle θ in standard position is given with a restriction on... Problem 34RE: An equation of the terminal side of an angle in standard position is given with a restriction on x.... Problem 35RE:
An equation of the terminal side of an angle θ in standard position is given with a restriction on... Problem 36RE Problem 37RE Problem 38RE Problem 39RE:
Give all six trigonometric function values for each angle θ. Rationalize denominators when... Problem 40RE: Give all six trigonometric function values for each angle . Rationalize denominators when... Problem 41RE Problem 42RE Problem 43RE Problem 44RE:
Give all six trigonometric function values for each angle θ. Rationalize denominators when... Problem 45RE Problem 46RE: Concept Check If, for some particular angle , sin 0 and cos 0, in what quadrant must lie? What... Problem 47RE Problem 48RE Problem 49RE Problem 50RE: Height of a Lunar Peak The lunar mountain peak Huygens has a height of 21,000 ft. The shadow of... Problem 1T:
1. Give the measures of the complement and the supplement of an angle measuring 67°.
Problem 2T Problem 3T Problem 4T Problem 5T Problem 6T Problem 7T Problem 8T:
Perform each conversion.
8. 74° 18′ 36″ to decimal degrees
Problem 9T: Perform each conversion. 45.2025 to degrees, minutes, seconds Problem 10T: Solve each problem. Find the angle of least positive measure that is coterminal with each angle. (a)... Problem 11T Problem 12T Problem 13T Problem 14T:
Sketch an angle θ in standard position such that θ has the least positive measure, and the given... Problem 15T: Sketch an angle in standard position such that has the least positive measure, and the given point... Problem 16T Problem 17T: Complete the table with the appropriate function values of the given quadrantal angles. If the value... Problem 18T Problem 19T Problem 20T:
20. Decide whether each statement is possible or impossible.
(a) sin θ = 1.5 (b) sec θ = 4 (c) tan... Problem 21T: Find the value of sec if cos=712. Problem 22T: Find the five remaining trigonometric function values of if sin=37 and is in quadrant II. Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Let 0 be an angle in quadrant II such that cos0=-2/5
Transcribed Image Text: **Trigonometric Values in Quadrant II**
Given:
Let \(\theta\) be an angle in quadrant II such that \( \cos \theta = -\frac{2}{5} \).
**Objective:**
Find the exact values of \(\csc \theta\) and \(\tan \theta\).
---
### Solution Steps:
**1. Identifying \(\sin \theta\) using Pythagorean Identity:**
Since \(\cos \theta = -\frac{2}{5}\), use the Pythagorean identity:
\[
\sin^2 \theta + \cos^2 \theta = 1
\]
\[
\sin^2 \theta + \left( -\frac{2}{5} \right)^2 = 1
\]
\[
\sin^2 \theta + \frac{4}{25} = 1
\]
\[
\sin^2 \theta = 1 - \frac{4}{25} = \frac{21}{25}
\]
\[
\sin \theta = \pm \sqrt{\frac{21}{25}} = \pm \frac{\sqrt{21}}{5}
\]
In quadrant II, \(\sin \theta\) is positive, so:
\[
\sin \theta = \frac{\sqrt{21}}{5}
\]
**2. Finding \(\csc \theta\):**
\[
\csc \theta = \frac{1}{\sin \theta} = \frac{5}{\sqrt{21}}
\]
**3. Finding \(\tan \theta\):**
Using the identity \(\tan \theta = \frac{\sin \theta}{\cos \theta}\):
\[
\tan \theta = \frac{\frac{\sqrt{21}}{5}}{-\frac{2}{5}} = -\frac{\sqrt{21}}{2}
\]
---
**Result:**
- \(\csc \theta = \frac{5}{\sqrt{21}}\)
- \(\tan \theta = -\frac{\sqrt{21}}{2}\)
These values were determined for \(\theta\) in quadrant II where \(\cos \theta = -\frac{2}{5}\), and confirm the relationships of \(\sin \theta\) and \(\tan \theta\) consistent with quadrant
Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.
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![**Trigonometric Values in Quadrant II**
Given:
Let \(\theta\) be an angle in quadrant II such that \( \cos \theta = -\frac{2}{5} \).
**Objective:**
Find the exact values of \(\csc \theta\) and \(\tan \theta\).
---
### Solution Steps:
**1. Identifying \(\sin \theta\) using Pythagorean Identity:**
Since \(\cos \theta = -\frac{2}{5}\), use the Pythagorean identity:
\[
\sin^2 \theta + \cos^2 \theta = 1
\]
\[
\sin^2 \theta + \left( -\frac{2}{5} \right)^2 = 1
\]
\[
\sin^2 \theta + \frac{4}{25} = 1
\]
\[
\sin^2 \theta = 1 - \frac{4}{25} = \frac{21}{25}
\]
\[
\sin \theta = \pm \sqrt{\frac{21}{25}} = \pm \frac{\sqrt{21}}{5}
\]
In quadrant II, \(\sin \theta\) is positive, so:
\[
\sin \theta = \frac{\sqrt{21}}{5}
\]
**2. Finding \(\csc \theta\):**
\[
\csc \theta = \frac{1}{\sin \theta} = \frac{5}{\sqrt{21}}
\]
**3. Finding \(\tan \theta\):**
Using the identity \(\tan \theta = \frac{\sin \theta}{\cos \theta}\):
\[
\tan \theta = \frac{\frac{\sqrt{21}}{5}}{-\frac{2}{5}} = -\frac{\sqrt{21}}{2}
\]
---
**Result:**
- \(\csc \theta = \frac{5}{\sqrt{21}}\)
- \(\tan \theta = -\frac{\sqrt{21}}{2}\)
These values were determined for \(\theta\) in quadrant II where \(\cos \theta = -\frac{2}{5}\), and confirm the relationships of \(\sin \theta\) and \(\tan \theta\) consistent with quadrant](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd774c29d-8836-4e46-9e38-7c9f22095e96%2F3c6512ab-5432-4d06-83bc-440c24fc67f4%2Fzr5b6xn_processed.jpeg&w=3840&q=75)
