Honors Pre-CalMrs. Cortez

x y = sin(x)

0 0

π/6 ½

π/2 1

5π/6 ½

π 0

7π/6 -½

3π/2 -1

11π/6 -½

2π 0

0 2 4 6

1.5

1.5

(0, 0)

Basic Graph of Sine Function

1 cycle ↔ PERIOD (how far it goes before it repeats)= 2π

The domain is the set of all real numbers. The range consists of all real numbers

from -1 to 1, inclusive. The sign function is an odd function, as

the symmetry of the graph is through the origin

The sine function is periodic, with period 2π.

The x-intercepts are …, -2π, -π, 0, π, 2π, 3π, …; the y-intercept is 0.

Properties continued

Now for the cosine graph

x y = cos(x)

0 1

π/3 ½

π/2 0

2π/3 - ½

π -1

4π/3 - ½

3π/2 0

5π/3 ½

2π 1

0 2 4 6

1.5

1.5

(0, 1)

The domain is the set of all real numbers. The range consists of all real numbers

from -1 to 1, inclusive. The sign function is an even function, as

the symmetry of the graph is with the y-axis.

The sine function is periodic, with period 2π.

y = d + asin(bx – c)

y = d + acos(bx – c)