Math 41
7.6 Graphs of Sine and Cosine Functions
Properties of the Sine Function y = sin x
1.
The domain is the set of all real numbers
2.
The range consists of all real numbers from -1 to 1, inclusive.
3.
The sine function is an odd function, as the symmetry of the graph with respect to the
origin indicates.
4.
The sine function is periodic, with period 2π.
5.
The x-intercepts are …,-2π, -π, 0, π, 2π, 3π,…; the y-intercept is 0.
6.
The maximum value is 1 and occurs at x =
…, -3π/2, π/2, 5π/2, 9π/2,…; the minimum
value is -1 and occurs at x = …,-π/2, 3π/2, 7π/2, 11π/2,….
Properties of the Cosine Function y = cos x
1.
The domain is the set of all real numbers.
2.
The range consists of all real numbers from -1 to 1, inclusive.
3.
The cosine function is an even function, as the symmetry of the graph with respect to the
y-axis indicates.
4.
The cosine function is periodic, with period 2π.
5.
The x-intercepts are x = …, -3π/2, -π/2, π/2, 3π/2, 5π/2,…; the y-intercept is 1.
6.
The maximum value is 1 and occurs at x = …, -2π, 0, 2π, 4π, 6π,…; the minimum value