Find exact value withouta csc21°secle9°- tan69°cota1° tor:
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°.
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Without using a calculator, can you help you find the exact value of this equation?
![The task is to find the exact value of the trigonometric expression without using a calculator:
\[ \csc 270^\circ - \sec 60^\circ - \tan 60^\circ \cdot \cot 270^\circ \]
1. **Cosecant (csc):**
- \(\csc 270^\circ = \frac{1}{\sin 270^\circ}\)
- Since \(\sin 270^\circ = -1\), \(\csc 270^\circ = -1\).
2. **Secant (sec):**
- \(\sec 60^\circ = \frac{1}{\cos 60^\circ}\)
- Since \(\cos 60^\circ = \frac{1}{2}\), \(\sec 60^\circ = 2\).
3. **Tangent (tan) and Cotangent (cot):**
- \(\tan 60^\circ = \sqrt{3}\).
- \(\cot 270^\circ = \frac{1}{\tan 270^\circ}\)
- Since \(\tan 270^\circ\) is undefined, \(\cot 270^\circ = 0\).
Using these values, substitute into the expression:
\[ \csc 270^\circ - \sec 60^\circ - \tan 60^\circ \cdot \cot 270^\circ = -1 - 2 - \sqrt{3}\cdot 0 = -3 \]
Thus, the exact value of the expression is \(-3\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c6652ef-ca76-4ad4-a995-eeca516ded87%2F684ee716-9ed7-4a3a-881d-4d2b487f7e82%2Fvlvg2ir_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The task is to find the exact value of the trigonometric expression without using a calculator:
\[ \csc 270^\circ - \sec 60^\circ - \tan 60^\circ \cdot \cot 270^\circ \]
1. **Cosecant (csc):**
- \(\csc 270^\circ = \frac{1}{\sin 270^\circ}\)
- Since \(\sin 270^\circ = -1\), \(\csc 270^\circ = -1\).
2. **Secant (sec):**
- \(\sec 60^\circ = \frac{1}{\cos 60^\circ}\)
- Since \(\cos 60^\circ = \frac{1}{2}\), \(\sec 60^\circ = 2\).
3. **Tangent (tan) and Cotangent (cot):**
- \(\tan 60^\circ = \sqrt{3}\).
- \(\cot 270^\circ = \frac{1}{\tan 270^\circ}\)
- Since \(\tan 270^\circ\) is undefined, \(\cot 270^\circ = 0\).
Using these values, substitute into the expression:
\[ \csc 270^\circ - \sec 60^\circ - \tan 60^\circ \cdot \cot 270^\circ = -1 - 2 - \sqrt{3}\cdot 0 = -3 \]
Thus, the exact value of the expression is \(-3\).
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