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

question 37

Multiple Choice

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) \(\mu _ { \mathrm { S } } = \tan \theta _ { \mathrm { S } }\)

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Definitions:

P(x = a)

The probability that the random variable X is equal to some value a.

Continuous Random Variable

A type of random variable that can take an infinite number of possible values in a continuum or interval on the number line.

P(x > a)

Represents the probability of a random variable X taking a value greater than a specific number a.

P(x = a)

Represents the probability that a discrete random variable X takes on a specific value a.