Homework Help is Here – Start Your Trial Now!
Math
Trigonometry
Assume sin(t) = -12 where π < t <3. Compute the following: csc (-t) = cos(t + 2) = tan(t) =

Assume sin(t) = -12 where π < t <3. Compute the following: csc (-t) = cos(t + 2) = tan(t) =

Trigonometry (11th Edition)
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
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
See similar textbooks
icon
Related questions
Question
**Trigonometric Function Calculation** Given the equation assuming \( \sin(t) = -\frac{1}{12} \) where \( \pi < t < \frac{3\pi}{2} \), compute the following trigonometric functions: 1. \(\csc(-t) = \) \(\boxed{\ \ \ \ \ \ \ }\) 2. \(\cos\left(t + \frac{\pi}{2}\right) = \) \(\boxed{\ \ \ \ \ \ \ }\) 3. \(\tan\left(\frac{\pi}{2} - t\right) = \) \(\boxed{\ \ \ \ \ \ \ }\) ### Explanation: - **Range of \( t \)**: This specifies that \( t \) is in the third quadrant of the unit circle since \( \pi \) to \( \frac{3\pi}{2} \) lies within the third quadrant. - **\(\csc(-t)\)**: Calculate using the definition \(\csc(x) = \frac{1}{\sin(x)}\). - **\(\cos\left(t + \frac{\pi}{2}\right)\)**: Use the co-function identity of sine and cosine. - **\(\tan\left(\frac{\pi}{2} - t\right)\)**: Use the co-function identity of tangent and cotangent. ***Note:*** The boxed areas are placeholders for the values to be calculated.
Transcribed Image Text:**Trigonometric Function Calculation** Given the equation assuming \( \sin(t) = -\frac{1}{12} \) where \( \pi < t < \frac{3\pi}{2} \), compute the following trigonometric functions: 1. \(\csc(-t) = \) \(\boxed{\ \ \ \ \ \ \ }\) 2. \(\cos\left(t + \frac{\pi}{2}\right) = \) \(\boxed{\ \ \ \ \ \ \ }\) 3. \(\tan\left(\frac{\pi}{2} - t\right) = \) \(\boxed{\ \ \ \ \ \ \ }\) ### Explanation: - **Range of \( t \)**: This specifies that \( t \) is in the third quadrant of the unit circle since \( \pi \) to \( \frac{3\pi}{2} \) lies within the third quadrant. - **\(\csc(-t)\)**: Calculate using the definition \(\csc(x) = \frac{1}{\sin(x)}\). - **\(\cos\left(t + \frac{\pi}{2}\right)\)**: Use the co-function identity of sine and cosine. - **\(\tan\left(\frac{\pi}{2} - t\right)\)**: Use the co-function identity of tangent and cotangent. ***Note:*** The boxed areas are placeholders for the values to be calculated.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry
Algebra and Trigonometry
Trigonometry
ISBN:
9781938168376
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS