Find the Exact Value $\sin \left( \sin ^ { - 1 } \frac { 3 } { 5 } - \cos ^ { - 1 } \frac { 1 } { 2 } \right)$

question 116

Multiple Choice

Find the exact value. $\sin \left( \sin ^ { - 1 } \frac { 3 } { 5 } - \cos ^ { - 1 } \frac { 1 } { 2 } \right)$

• A) \(3 / 10\)
• B) \(2 \sqrt { 3 } / 5\)
• C) \(( 3 - 4 \sqrt { 3 } ) / 10\)
• D) \(( 3 - \sqrt { 2 } ) / 10\)
• E) \(( 3 - 4 \sqrt { 3 } ) / 5\)

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Definitions:

Deltoid

A large triangular muscle covering the shoulder joint and responsible for lifting the arm and giving the shoulder its range of motion.

Teres Minor

A small muscle of the rotator cuff that assists in rotating the arm laterally and stabilizes the shoulder joint.

Biceps Brachii

A muscle of the upper arm that flexes the forearm and is involved in moving the shoulder and elbow.

Ventral Root

The part of a spinal nerve that emerges from the anterior portion of the spinal cord, containing motor fibers that transmit neural signals from the spinal cord to the body muscles.