Taylor's Blog

In the following lesson I shall be informing you on lesson 7.1 of my Advanced Math class.



There are two units of measure for angles. They are degrees and radians.



If you want to convert degrees to radians you must use the following formula.



degrees x PI/180



An example of this would be the following problem.



Convert 15 degrees to radians.



15 degrees x PI/180 1st. Place the degrees ,15, into its proper location in the equation.



15PI/180 You will then multiply 15 degrees and PI/180, or 15 X PI to get this answer.



PI/12 You will then divide 180 into 15,or reduce, and put it in a fraction form. This is your answer.



IMPORTANT NOTE: PI IS LIKE X A VARIABLE SO DON'T PUT IT INTO YOUR CALCULATOR OR YOU WILL GET THE WRONG ANSWER!



If you want to convert radians to degrees you would use this formula.



rads x 180/PI



An example of this equation has been given.



Convert 12PI to degrees.



12PI X 180/PI First place your radians into its proper place in the equation.



12P/I X `180/P/I Since 12PI and 180/PI both have PI and one is in the lower part of the fraction and the other is in the upper part of the fraction. We can cancel out PI in the equation.



12 X 180 You will then multiply 12 times 180.



2160 degrees This is what your answer should be.



IMPORTANT NOTE: MAKE SURE TO PUT THE DEGREES MARK OR IT WILL BE WRONG!!



There are some angles that are called coterminal angles. Coterminal means that the degrees 'spins' around the angle in this usage.



If you are asked to find the positive or/and negative form of a coterminal angle for degrees you will use this formula.



degrees +/- 360 degrees



Yet, if you are asked to find the positive or/and negative form of a coterminal angle for radians you would use this formula.



rads +/- 2 PI



An example of these situations are as followed.



Find a positive coterminal angle of 12 degrees.



12 degrees = 360 degrees First, you will place 12 degrees into the equation and since we need it to be positive we will add 360 to it.



372 degrees This is the correct answer that you should have gotten after adding 360 to 12.



Find the negative coterninal angle of 18 degrees.



18 degrees - 360 degrees First place 18 into its correct place in the equation and since we need to find the negative coterminal angle we will subtract 360 from 18 instead of adding it.



-342 degrees This is the negative answer that you should have gotten.



Now lets find the positive coterminal angle for 4PI/6.



4PI/6 + 2PI First place the 4PI/6 in its correct location in the equation and since we need to find the positive coterminal angle you will add 2Pi.



4pi/6 + 12pi/6 Now convert the 2PI so that you can add correctly. Do this by multiplying 2 by 6 and placing a six in the denominator.



16PI/6 After you do that you add the fractions together.



8PI/3 Then you reduce the fraction by dividing it by two.



Now lets find the negative coterminal angle of 8PI/6.



8PI/6 - 2PI First place 8Pi/6 in its proper location in the equation and since we are finding the negative coterminal angle you will subtract 2PI instead of adding it.



8PI/6 - 12PI/6 Than you will make 2PI into a fraction by placing it over 6 and multiplying it by 6.



-4PI/6 You will then subtract and get this answer.



-2PI/3 Then you will reduce the fraction by diving it by two and this is your answer.



Now lets learn how to get minutes and seconds from our equations.

ab.cd
.cd x 60 = y minutes y'
y x60 = z seconds z''

This is the formula that we will be using in the following problem.

Covert 15.699 degrees to minutes and seconds.

.699 x 60= 41.94 First we will put .699 into the equation because it is after the decimal point. We will then multiply it by 60 so that we can get 41.94. Since we have another decimal point we must continue the equation.

.94 x 60= 56.4 We will take the numbers after the decimal and multiply them by 60. Since we don't need the .4 you will simply drop it, since we just need seconds.

15 degrees 41' 56'' This is what your answer should be and what it should look like.

The final thing that you must know is how to convert the minutes and seconds back into degrees. You will use the following formula in order to do this.

x'=minutes y''= seconds

x/60 = y/3600= degrees

Now use it to solve the following problem.

Convert 10 degrees 56' 78'' in to degrees.

56/60 = 78/3600 First place the seconds and minutes in their appropriate location in the formula.

.955 Then you add the fractions together and convert the fraction that you may have gotten if you are doing this by hand into a decimal.

10.955 degrees Than you simply place the decimal behind the number and that is how you get your answer.

That is all the equations, formula and information that we learned in section 7.1. Until my next blog BYE.