Chapter 10 - NCPN

The Cosine Function
The cosine function y = cos θ gives the corresponding x-coordinate where
the terminal side of the angle intersects the unit circle. So the graph of the
cosine function is a sine curve that is shifted to the left. A phase shift is a
horizontal translation of a periodic function. The cosine and sine functions
have graphs that are 90° or ≠ radians out of phase.
2
Characteristics of Cosine Functions
The generalized cosine function y = acos bθ, with a ≠ 0,
b > 0, and θ in radians has the following properties:
• the amplitude of the function is |a|.
• the number of cycles in the interval from 0 to 2π
radians is b.
• the period of the function is 2≠ b .
The graphs of the cosine (blue) and sine (purple) functions are defined for
θ values that are negative and for θ values that are larger than 360°. The
measure of an angle is positive when the rotation is counterclockwise. The
measure of an angle is greater than 360° when more than one full rotation of
the unit circle has been completed. Every angle that is negative or is greater
than 360° is in the same position as an angle between 0° and 360°. Thus, the
sine curve repeats itself as θ → ∞ and as θ → –∞.
456 Chapter 10 Trigonometric Functions and Identities