122-28029 Parallax Inc, 122-28029 Datasheet - Page 112

• Manufacturer Part Number: 122-28029
• Description: GUIDE STUDENT SMART SENSORS
• Manufacturer: Parallax Inc

Specifications of 122-28029

• Accessory Type: Manual
• Product: Microcontroller Accessories
• Lead Free Status / RoHS Status: Contains lead / RoHS non-compliant
• For Use With/related Products: Smart Sensors
• Lead Free Status / RoHS Status: Lead free / RoHS Compliant, Contains lead / RoHS non-compliant

Page 100 · Smart Sensors and Applications
Note from the equations for Figure 3-27 that the x value can be at most the same as h
when θ = 0°. Likewise, the y value can be at most h when θ = 90°. For angles between 0
and 90°, the ratio of x/h and y/h are both less than 1. It doesn't matter how large the
triangle is, the ratio will always be between 1 and 0.
The unit circle is a common device for describing the sine and cosine functions. The
triangle's hypotenuse becomes the radius of the circle. The unit circle is so named
because the length of the hypotenuse is 1 (one unit). As the hypotenuse is rotated
counterclockwise, the angle θ becomes larger, or smaller if it is rotated clockwise. The
cosine is determined by drawing a vertical line from the point where the hypotenuse
meets the circle down (or up if the hypotenuse is below) to the x-axis. Whatever the x
value is, that's the cosine. The sine of the angle is determined by drawing a line from the
end of the radius horizontally to the y-axis.
Figure 3-28: Unit Circle Sine and Cosine Examples
a.
b.
c.
The range from 0 to 90° is the unit circle's Quadrant 1. When θ is in Quadrant 1, both the
cosine and sine of the angle will be positive numbers. When θ is between 90 and 180°
(Quadrant 2), the cosine becomes negative but the sine is still positive. In Quadrant 3,
both sine and cosine are negative, and in Quadrant 4, the sine is still negative but cosine
is positive again. Notice in Figure 3-28 (c) that a negative value of θ (between 0 and
−90) can be in Quadrant 4 just as a value between 270 and 360°. One other thing to keep
in mind here is that the minimum value for both sine and cosine is −1, and the maximum
value is 1. For example, when θ = 0°, cos θ = 1, and sin θ = 0. If θ = 90°, sin θ = 1 and
cos θ = 0. At θ = 180°, cos θ = −1 and sin θ = 0.