Notes for Homework 5, due Monday, Feb. 27

Degrees to DMS: Most scientific calculators has a function that will take a decimal number and convert it to degrees, minutes and seconds. Degrees and minutes will be whole numbers, but seconds might be a decimal. Not all the calculators round the seconds decimal to the same level, so I ask that it be rounded to the nearest tenth.

Example: if we take the inverse sine of 1/3, we get 19.47122063...°,which I ask to be rounded to four places after the decimal, so 19.4712°. If we take the unrounded answer and find the DMS conversion, we get 19° 28' 16.394" when using the TI-83 and 19° 28' 16.4" when using the TI-30XIIs. Because these calculators made by the same company don't round to the same level, I ask for the rounding to be to the nearest tenth of a second.

Note: Inverse sine and inverse tangent of negative numbers give negative angles in Quadrant IV. Add 360° to get a number between 0° and 360°.

Degrees to radians, both as a decimal number and a decimal time pi. At this point in the semester, your calculator should be DEGREE mode, so on any of the problems on the homework should start with taking the requested inverse trig function, converting the answer to a positive angle if necessary. Whether you have the angle in decimal degrees or DMS, you can now multiply the answer by pi/180 to get radians as a decimal number. In this case, you should get 0.339836909..., which I ask to be rounded to .3398. If you divide this by pi, you get .108173448..., which is the decimal number to be multiplied by pi. This means the four answers to the inverse sine of 1/3 are

Decimal degrees: 19.4712°
DMS: 19° 28' 16.4"
Radians: .3398
Radians as a multiple of pi: .1082pi