The Function $y = 5 \cos \left( 1.5 t - \frac { \pi } { 3 } \right)$

question 49

Essay

The function $y = 5 \cos \left( 1.5 t - \frac { \pi } { 3 } \right)$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find the amplitude, period, and frequency of motion and sketch a graph of the function over one complete period.

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Definitions:

Cognitive Behavioral Techniques

Strategies used in cognitive-behavioral therapy to change negative thought patterns and behaviors into more positive ones.

Schizotypal Personality Disorder

A mental condition characterized by severe social anxiety, thought disorder, paranoid ideation, derealization, transient psychosis, and often unconventional beliefs.

Challenging Perceptions

The act of questioning or scrutinizing commonly held beliefs or views to gain a deeper understanding or identify inaccuracies.

Cognitive Therapy

A form of psychotherapy that focuses on changing unhelpful or destructive thought patterns in order to improve emotional regulation and develop personal coping strategies.