Problem 1: Add/ Subtract the following angles by hand (no excel spread sheet for this part) as indicated and express the result in degrees, minutes and seconds of arc:

Angle1 = 103 43 24 Angle2 = 63 48 59

Angle3 = 113 33 47 Angle4 = 53 27 36

Add Angle1 to Angle2 = _______ _______ ______

Subtract Angle 4 from Angle3 = _____ ______ ______

Method to solve the above problem with an excel spread sheet we will illustrate how to work this on a spread sheet. As a first step we need to add the seconds part of the angles. We need to check if it is more than 60 of arc and find out how many minutes are there in the result of adding the seconds part. Recall the TRUNC function form the previous lab which provides the integer part of a decimal number. If we divide the result of adding seconds part of the two angles we will get a decimal number and the integer part will be the number minutes that we need to account for when we work on the minutes part of the angles. To get the seconds part after taking out minutes, is obtained by using the result adding seconds part and subtract form this 60 x the number of minutes [TRUNC(added seconds part)]

Step 1 adding seconds part enter in cell E4 formula = E2+ E3 60*TRUNC((E2+F3)/60)

Step2 Adding minutes parts form angle 1 and angle 2 to the carried over minutes from the seconds part

Enter in cell D4 the formula

= D2+D3+ TRUNC((E2+E3)/60) - 60*TRUNC((D2+D3+ TRUNC((E2+E3)/60))/60)

This will give you the number of Minutes of arc in the added result and the carry over number of hours is given by = TRUNC((D2+D3+ TRUNC((E2+E3)/60))/60)

Then you need to add the number of degrees of arc in each angle with the above carry over degrees

So you enter in cell C4 the formula

= C2 + C3 + TRUNC((D2+D3+ TRUNC((E2+E3)/60))/60)

	A	B	C	D	E
1	#	Angle Label	Degrees	Minutes	Seconds
2	1	Angle1
3	2	Angle2
4	3	Angle1 + Angle2

Problem 2: Do the same mathematical operation by using decimal representation of the angles same angles listed above. First convert each angle into decimal representation and enter below and then do the mathematical operation as listed in a) and b) below

Angle1:___________ Angle2: __________ Angle3: _________ Angle4: __________

Add Angle1 and Angle2 = _____________

Subtract Angle4 from Angle3 = ________________

Open a excel spread sheet and enter the values of each of these angle in three different columns in a row with the column title as Degrees, Minutes and Seconds and in the next column write a function to calculate the angle in decimal form and then copy and paste the same formula for next three rows of the 6^th column which will automatically calculate the decimal part for the next three angles in the table. Then write the formula for subtraction and addition for the 7^th and 8^th column. Save the spread sheet temporarily. Remember to convert the angles to decimal part. For this all that you have to do is add angle in degrees + angles in minutes/60 + angles in seconds of arc/3600. Ensure to carry over this to six decimal places to account for an accuracy of 1 sec of arc

#	Angle Label	Degrees	Minutes	Seconds	Angle in decimal units	Angle1+ Angle 2 (use values in decimal form in column 6)	Angle3 Angle 4 (use values in decimal form in column 6)
1	Angle1
2	Angle2
3	Angle3
4	Angle4

Go to page 2 and resume reading and then do the next problem

Problem 3: Calculate the number of arc seconds in one radian (six significant figures). This number has a special significance in Astronomical distance measurements.

1 Radian = ____________________ arc seconds

Note: Addition and subtraction operations, with Radian measure, are same as doing it with real numbers.

Go to page 3 and resume reading and do the next set of problems

Problem 4: Convert each of the angles listed in problem1 into radians and perform the mathematical operation that is asked in that problem (use the decimal representation of angles). First enter the angles in radians and then perform the operations as listed in c) and d) below.

Angle1:___________ Angle2: __________ Angle3: _________ Angle4: _______

Add Angle1 and Angle2 = _____________

Subtract Angle4 from Angle3 = ________________

Retrieve the saved spread sheet copy the data onto the 2^nd sheet and insert one column next to column 6 and add the label for that column as angle in radian Units and replace the words in the next two columns

From (use values in decimal form in column 6) to (use values in radian form in column 7)

Go to page 3 and resume reading

Problem 5: Compute the following and express the result in d h m s (use d only when it is greater than a day otherwise omit it)

Time1 = 19^h 23^m 14^s Time2 = 14^h 32^m 19^s Time3 = 9^h 21^m 54^s

Time4 = 10^h 23^m 14^s Time5 = 9^h 33^m 54^s Time6 = 23^h 23^m 14^s

Add Time1 to Time2 =

Add Time3 to Time4 =

Subtract Time 5 from Time6 =

Problem 6: Repeat the above (problem 5) computation using decimal representation of hours only (note: if the total of the time intervals is more than 24 hours do not convert into days keep the result in hours). Make sure you convert each of the above time into decimal representation and then perform the operation listed above.(keep only 4 digits after the decimal). First step is to convert the times into decimal form and enter next to the quantity listed below and then perform the mathematical operations as listed in A), B) and C)

Time1: Time2: Time3:

Time4: Time5: Time6:

Add Time1 to Time2 = ______________________

Add Time3 to Time4 = ______________________

Subtract Time 5 from Time6 = _______________________

Problem 7: convert each of time units given in problem 6 into angular units in Degrees, Minutes of arc and Minutes of Seconds

Example: Follow the procedure carried out in this part to the other 5 Time units given in the previous problem

Given Time1 = 19^h 23^m 14^s

First step convert the seconds of timw in to Arc seconds

(Use the fact that 1 Second of time unit = 15 Arc Seconds)

So 14^s = 14^s x 15 arc sec/s = 210 = 3 30 (we need to convert every 60 to a minute of arc if it is more than 60)

Second Step convert the minutes of time to minutes of arc

We have 23^m = 23^m x 15 arc min/m = 345

To this we need to add the number Min of arc from the step1 thus we have 348 which is = 5 48 (we need to convert every 60 to a degree if it is more than 60)

Third Step convert hours of time to degrees of arc

We have 19^h = 19^h x15 degree/hour = 285 to this we need to add the number of degrees from step 2 thus we have 290

Hence 19^h 23^m 14^s corresponds to 290 48 30