Applications of trigonometric functions
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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.

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Objectives
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
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
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


Applications of trigonometric functions 1334040

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.


Applications of trigonometric functions 1334040

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.


Applications of trigonometric functions 1334040
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


Applications of trigonometric functions 1334040

Solve the triangle equation below, where

C

a = 10

b = 12

A

B

c = 16


Determine if the following measurements produce one triangle two triangles or no triangles
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 triangles1
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 triangles2
Determine if the following measurements produce one triangle, two triangles, or no triangles.

a = 20, b = 15, A = 40