HP 30s Quick Start Manual

Angle Measurements Time Measurements Practice Solving Problems Involving Angles and Times

Angle measurements The amount of turning between two rays with a common origin, or the measure of change of direction, is what we call an angle. Angles cannot be measured in meters or yards. As measures of the amount of turning, we use degrees, radians and grads. A degree is one 360th of a complete turn and its symbol is º. Just like a meter which has multiples and submultiples (e.g. kilometer, millimeter, etc), degrees are broken down into minutes and seconds. The minute (‘) is one sixtieth of a degree, and the second (‘‘) is one sixtieth of a minute. The radian is defined as the angle subtended by an arc of a circle of length equal to its radius (see figure 1). Its symbol is C (but this symbol is not widely used). Note that the counterclockwise direction of turning is taken to be positive. Grads are a measure of angle equal to one hundredth of a right angle. Grads are also known as gradians and grades. Angle units can be easily converted since: grads degrees radians 400 360 2 = = π It is important to understand that there are two ways of expressing an angle in degrees: using decimal degrees and using degrees, minutes and seconds. In decimal degrees, an angle is simply given as 33.5 degrees, that is to say, 33 degrees and a half. In the degrees, minutes, seconds (or DMS) format, the same angle is 33 degrees, 30 minutes. The HP 30S can work with angles in either measurement system and provides the DRG ( c) and DMS ( —A) menus to convert between them. It also has the�DMS function (—A

The entry line contains 25º. When this is evaluated by the ykey, the HP 30S will convert 25º into the current angle unit, i.e. radians. Answer: 0.436332313 radians. Example 2: Convert 25º into grads. Solution: First of all, we have to set the angle mode to the unit into which we want to convert, i.e. grads. Press c@y (assuming RAD was the current mode) Note that the entry line now contains 25º again—the last calculation entered or the one being edited— so we just have to press y to do the conversion. Answer: 27.77777778 grads or 9 27 7 grads (press —Iy to express the result as a mixed number). Example 3: Convert an angle of 3 2π radians into decimal degrees. Solution: Since the target unit is degrees, set the angle mode to degrees by pressing: c@y. The entry line still contains 25º from previous examples. Press o to clear it. Now enter 2π 3 and add a small r from the DMS menu to indicate that this quantity is expressed in radians: r2x/3s—A@@@y The entry line now reads r) ( 2π 3 . Parentheses are necessary because the º, ‘, ‘’, and functions take precedence over the division function. Press yand the result line will contain the same value but expressed in decimal degrees. r g Answer: 120º Example 4: Add 120º to .1r and express the result in both decimal degrees and in the DMS format. 4 Solution: 120º is already stored in ANS from the previous example, so press: +4.1—A@@@yy It returns the sum expressed in decimal degrees. To express this number in the DMS format, use the �DMS function of the DMS menu. You need not reenter its argument, since it is taken from the ANS register, simply press: —A

Example 5: Convert an angle of 2.3714 degrees into DMS. Solution: Assuming that the current angle mode is still set to degrees, press: 2.3714—A