Chapter 10 - NCPN

Lesson 10.4 Graphing Trigonometric
Functions
Objectives
Graph trigonometric
functions.
A floating object is observed to
move in circles when waves oscillate
harmoniously in deep water. When
the object is placed in deeper water, it
moves along a circular path. The size
of the circular path gets smaller and
smaller in diameter at different water
depths. At a certain depth, the object
would stand still. This is the wave’s
base, which is exactly half the wave’s
length. An oceanologist is studying the
position of a leaf floating on the surface
of a wave. The oceanologist describes
the motion of the leaf by the function y = 1.5sin 2θ. The oceanologist
wants to graph this function to display the motion of the leaf.
The Sine Function
Recall that the function, y = sin θ, takes an angle measure as its input
and gives the corresponding y-coordinate where the terminal side of
the angle intersects the unit circle. So the domain of the function is
the set of all angle measures, θ, and the range is between –1 and 1.
The graph of a sine function is called a sine curve.
The amplitude of a function is half the positive difference between
its maximum and minimum values. So the amplitude of the function
y = sin θ is 1. The period of a function is the horizontal length of one
cycle. The function y = sin θ completes one full cycle as its output
values range from 0 to 1 to –1 and then back to 0. So the period of the
standard sine curve is 360° or 2π radians.
454 Chapter 10 Trigonometric Functions and Identities