Table 20.6 summarizes the values for the sine, cosine, and
tangent functions of common angles. The triangles that yield these values are
seen in Figures 20.54A, 20.54B, 20.55, and 20.56. Notice that the angles are
given in degree and radian form. Radian measure is discussed in Chapter 7.
When using a scientific calculator to
find values for trigonometric functions, make sure the calculator is set to DEGREE
mode for angles in degrees or RADIAN mode forangles in radians.
The values are expressed as fractions with rationalized
denominators. This table is useful to commit to memory.
Now that we have established how to find values for
trigonometric functions of any angle, we can generate graphs for trigonometric
functions.
Sine Function
Graph
The graph for the sine function between 0 and 360 degrees is
given in Figure 20.61. The data for the graph are from Table 20.6
The
amplitude
of the sine
graph varies between –1 and +1. The sine function is
periodic
, repeating every 360 degrees.
Cosine Function
Graph
The graph for the cosine function between 0 and 360 degrees is
given in Figure 20.62. The data for the graph are from Table 20.6.
As with the sine graph, the amplitude of the cosine graph varies
between –1 and +1. The cosine function is also periodic and repeats every 360
degrees with a 90-degree offset to the left, or phase shift, from the sine
graph.
Tangent Function
Graph
The graph for the tangent function between 0 and 360 degrees is
given in Figure 20.63. The data for the graph are from Table 20.6.
Now that we have established how to find values for
trigonometric functions of any angle, we can generate graphs for trigonometric
functions.
Sine Function
Graph
The graph for the sine function between 0 and 360 degrees is
given in Figure 20.61. The data for the graph are from Table 20.6
The
amplitude
of the sine
graph varies between –1 and +1. The sine function is
periodic
, repeating every 360 degrees.
Cosine Function
Graph
The graph for the cosine function between 0 and 360 degrees is
given in Figure 20.62. The data for the graph are from Table 20.6.
As with the sine graph, the amplitude of the cosine graph varies
between –1 and +1. The cosine function is also periodic and repeats every 360
degrees with a 90-degree offset to the left, or phase shift, from the sine
graph.
Tangent Function
Graph
The graph for the tangent function between 0 and 360 degrees is
given in Figure 20.63. The data for the graph are from Table 20.6.
F
IGURE
20.63
Graph of tangent function
between 0 and 360 degrees
The tangent function approaches positive infinity for angles
less than, but very close to, 90 degrees and 270 degrees; it approaches
negative infinity for angles greater than, but very close to, 90 and 270
degrees. At 90 and 270 degrees, the function is
undefined
. The dashed lines through 90 and
270 are called
asymptotes
.