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) =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 4E
See similar textbooks
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
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS