5t cot 4
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°.
Related questions
Question
Find exact value :
![The image shows the mathematical expression for the cotangent function:
\[ \cot\left(\frac{5\pi}{4}\right) \]
This expression involves the cotangent trigonometric function applied to the angle \(\frac{5\pi}{4}\) radians.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58499046-086a-4660-af23-4374372978d6%2Fd1acc2d2-4ad2-4ff9-a35d-6bd4b70fcf2b%2Frvov9dl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows the mathematical expression for the cotangent function:
\[ \cot\left(\frac{5\pi}{4}\right) \]
This expression involves the cotangent trigonometric function applied to the angle \(\frac{5\pi}{4}\) radians.
![The expression shown is the cosecant function applied to the angle \(-\frac{3\pi}{2}\). The cosecant function is the reciprocal of the sine function. Therefore, it can be expressed as:
\[ \text{csc}(\theta) = \frac{1}{\sin(\theta)} \]
In this expression, \(\theta\) is equal to \(-\frac{3\pi}{2}\).
Let's break it down:
1. **\(-\frac{3\pi}{2}\)**: This represents an angle in radians. Radians are a unit of angular measure used in many areas of mathematics. One full rotation around a circle is \(2\pi\) radians. Therefore, \(-\frac{3\pi}{2}\) is equivalent to rotating \(270^\circ\) clockwise or \(90^\circ\) counterclockwise from the negative x-axis.
2. **Cosecant Function (\(\text{csc}\))**: This is a trigonometric function. It's undefined when the sine of the angle is zero because division by zero is undefined in mathematics.
To evaluate \(\text{csc}\left(-\frac{3\pi}{2}\right)\), we need to find \(\sin\left(-\frac{3\pi}{2}\right)\):
- The sine of \(-\frac{3\pi}{2}\) is -1.
Thus, \(\text{csc}\left(-\frac{3\pi}{2}\right)\) evaluates to \(-1\) because:
\[ \text{csc}\left(-\frac{3\pi}{2}\right) = \frac{1}{\sin\left(-\frac{3\pi}{2}\right)} = \frac{1}{-1} = -1 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58499046-086a-4660-af23-4374372978d6%2Fd1acc2d2-4ad2-4ff9-a35d-6bd4b70fcf2b%2Fa22t5j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The expression shown is the cosecant function applied to the angle \(-\frac{3\pi}{2}\). The cosecant function is the reciprocal of the sine function. Therefore, it can be expressed as:
\[ \text{csc}(\theta) = \frac{1}{\sin(\theta)} \]
In this expression, \(\theta\) is equal to \(-\frac{3\pi}{2}\).
Let's break it down:
1. **\(-\frac{3\pi}{2}\)**: This represents an angle in radians. Radians are a unit of angular measure used in many areas of mathematics. One full rotation around a circle is \(2\pi\) radians. Therefore, \(-\frac{3\pi}{2}\) is equivalent to rotating \(270^\circ\) clockwise or \(90^\circ\) counterclockwise from the negative x-axis.
2. **Cosecant Function (\(\text{csc}\))**: This is a trigonometric function. It's undefined when the sine of the angle is zero because division by zero is undefined in mathematics.
To evaluate \(\text{csc}\left(-\frac{3\pi}{2}\right)\), we need to find \(\sin\left(-\frac{3\pi}{2}\right)\):
- The sine of \(-\frac{3\pi}{2}\) is -1.
Thus, \(\text{csc}\left(-\frac{3\pi}{2}\right)\) evaluates to \(-1\) because:
\[ \text{csc}\left(-\frac{3\pi}{2}\right) = \frac{1}{\sin\left(-\frac{3\pi}{2}\right)} = \frac{1}{-1} = -1 \]
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