Find the Exact Value of the Expression Using the Provided $\sin ( s - t )$

question 300

Multiple Choice

Find the exact value of the expression using the provided information.
-Find $\sin ( s - t )$ given that $\cos s = \frac { 1 } { 3 }$ , with $s$ in quadrant $I$ , and $\sin t = \frac { 1 } { 4 }$ , with $t$ in quadrant II.

• A) \(\frac { - 2 \sqrt { 30 } - 1 } { 12 }\)
• B) \(\frac { - 30 \sqrt { 2 } - 1 } { 12 }\)
• C) \(\frac { - 12 \sqrt { 30 } - 1 } { 2 }\)
• D) \(\frac { - 12 \sqrt { 2 } - 1 } { 30 }\)

---

Definitions:

Federal Government

The national government of a federation, which holds the authority to govern matters that affect the entire country.

Church of England

The primary state church in England, which is a part of the worldwide Anglican Communion; it has its roots in the 16th-century Reformation.

Federal Laws

Laws created and enforced by the federal government of a country.

Limitations

Legal restrictions, often related to the time within which legal proceedings must be initiated.