Solve the Problem $\theta _ { \mathrm { S } }$

Solve the problem.
-A wooden block sitting at rest on a flat, level board will just begin to slide when the board is tilted up to a critical angle of inclination, $\theta _ { \mathrm { S } }$ . An experiment that determines this critical angle can be used to find the coefficient of static friction, $\mu _ { \mathrm { S } }$ , for the block on the board by using the relation $\mu _ { \mathrm { S } } = \frac { \sin \theta _ { \mathrm { S } } } { \cos \theta _ { \mathrm { S } } }$ . Rewrite this relation using a quotient identity.

A) $\mu _ { \mathrm { S } } = \cot \theta _ { \mathrm { S } }$
B) $\mu _ { \mathrm { S } } = \sec \theta _ { \mathrm { S } }$
C) $\mu _ { \mathrm { S } } = \tan ^ { 2 } \theta _ { \mathrm { S } }$
D) $\mu _ { \mathrm { S } } = \tan \theta _ { \mathrm { S } }$

Correct Answer:

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