Write the Expression in Terms of Sine and Cosine, and Simplify

question 253

Multiple Choice

Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
-The power dissipated in an electric circuit is given by the expression $\mathrm { P } = \mathrm { RI } ^ { 2 }$ , where $\mathrm { R }$ is the resistance of the circuit and $I$ is the current through the circuit. For a sinusoidal alternating current, the current might be represented by the relation $\mathrm { I } = \mathrm { A } \sin ( 2 \pi \mathrm { ft } )$ , where $\mathrm { A }$ is the amplitude, $\mathrm { f }$ is the frequency, and $t$ is time. Write an expression for $P$ involving the sine function, and use a fundamental identity to write $P$ in terms of the cosine function.

• A) \(P = R A ^ { 2 } \sin ^ { 2 } ( 2 \pi f t ) ; P = - R A ^ { 2 } \cos ^ { 2 } ( 2 \pi f t )\)
• B) \(P = R A \sin ^ { 2 } ( 2 \pi f t ) ; P = R A - \cos ^ { 2 } ( 2 \pi f t )\)
• C) \(P = R A ^ { 2 } \sin ^ { 2 } ( 2 \pi f \mathrm { ft } ) ; P = R A ^ { 2 } - R A ^ { 2 } \cos ^ { 2 } ( 2 \pi f t )\)
• D) \(P = R A \sin ^ { 2 } ( 2 \pi f \mathrm { ft } ) ; P = R A - R A \cos ^ { 2 } ( 2 \pi f t )\)

Explain the process and importance of selecting optimal goals over merely acceptable ones.

Understand the use of heuristics in decision making.

Describe the importance of knowledge management in delivering timely and relevant information.

Acknowledge the potential for biases and political influences in the decision-making process.

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Definitions:

Median

The middle value in a list of numbers, which divides the dataset into two halves.

Mode

The value that occurs most frequently in a given set of data.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values; a low standard deviation indicates that the values tend to be close to the mean of the set.

Variability

Refers to the degree of difference or deviation from the mean within a set of data.