Use Fundamental Identities to Find the Exact Values of the Trigonometric

question 25

Multiple Choice

Use fundamental identities to find the exact values of the trigonometric functions for the given conditions. $\csc \theta = 7 \text { and } \cot \theta < 0$

• A) \(\begin{array} { l }
• \sin \theta = - \frac { \sqrt { 48 } } { 7 } , \quad \cos \theta = \frac { 1 } { 7 } , \quad \tan \theta = - \frac { 1 } { \sqrt { 48 } } \\
• \cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = 7
• \end{array}\)
• B) \(\begin{array} { l }
• \sin \theta = - \frac { 1 } { 7 } , \quad \cos \theta = \frac { \sqrt { 48 } } { 7 } , \quad \tan \theta = \frac { 1 } { \sqrt { 48 } } \\
• \cot \theta = \sqrt { 48 } , \quad \sec \theta = \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = - 7
• \end{array}\)
• C) \(\begin{array} { c c }
• \sin \theta = \frac { 1 } { 48 } , \quad \cos \theta = - \frac { \sqrt { 48 } } { 48 } , \quad \tan \theta = - 1 \\
• \cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = 48
• \end{array}\)
• D) \(\begin{array} { c }
• \sin \theta = \frac { 1 } { 7 } , \quad \cos \theta = - \frac { \sqrt { 48 } } { 7 } , \quad \tan \theta = - \frac { 1 } { \sqrt { 48 } } \\
• \cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = 7
• \end{array}\)
• E) \(\begin{array} { l }
• \sin \theta = - \frac { 1 } { 48 } , \quad \cos \theta = \frac { \sqrt { 48 } } { 7 } , \quad \tan \theta = - \frac { 1 } { \sqrt { 48 } } \\
• \cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 48 } { \sqrt { 48 } } , \quad \csc \theta = - 7
• \end{array}\)

---

Definitions:

Frontier Settlers

Individuals or families who moved to the edge of settled territories to establish a new life, often facing harsh conditions and conflicts with indigenous people.

Anti-Federalists

Opponents of the ratification of the U.S. Constitution in 1787-1788, who favored stronger state governments and feared a too powerful federal government.

Proclamation of 1763

Royal directive issued after the French and Indian War prohibiting settlement, surveys, and land grants west of the Appalachian Mountains; caused considerable resentment among colonists hoping to move west.

Articles of Confederation

The original constitution of the United States, ratified in 1781, which was eventually replaced by the U.S. Constitution in 1789 due to its weakness in central governance.