Applications of Trigonometric Functions Section 4.8

Objectives Model simple harmonic motion Determine the maximum displacement, frequency, and period of an object in simple harmonic motion Apply Law of Sines and Law of Cosine to solve triangles.

Vocabulary simple harmonic motion – up and down oscillations (ignoring friction and resistance) equilibrium position – rest position maximum displacement - amplitude period – how long it takes for the motion to go through one complete cycle frequency – one divided by the period

Formulas simple harmonic motion used when the object is at its greatest distance from rest position at the origin used when the object is at its rest position at the origin

An object is attached to a coiled spring. The object is pulled down 6 centimeters from the rest position and then released. The period of the motion is 4 seconds. Write an equation for the distance of the object from it’s rest position t seconds.

An object is attached to a coiled spring. The object is initially at rest position and then pulled down 5 centimeters from the rest position and then released. The period of the motion is 1.5 seconds. Write an equation for the distance of the object from it’s rest position t seconds.

An object in simple harmonic motion is described by the equation below, where t is measured in seconds and d is in inches. Find each of the following The maximum displacement The frequency The time required for one cycle

Solve the triangle AB C a = 10 c = 16 b = 12

Determine if the following measurements produce one triangle, two triangles, or no triangles. a = 10, b = 40, A = 60 

Determine if the following measurements produce one triangle, two triangles, or no triangles. a = 42.1, b = 37, A = 112 

Determine if the following measurements produce one triangle, two triangles, or no triangles. a = 20, b = 15, A = 40 