When do you use Deg, Rad and Gra and what do they mean?

Deg, Rad and Gra are three angle modes on scientific calculators. Beginners don’t usually know the use of them nor their definition.  They are very simple to understand and also to use when being explained briefly and as simple as possible.

On a scientific calculator “D” or “DEG” means the current angle mode is in degrees. A degree is a complete revolution of 360 or you could say it is 1/360 of the circumference of a circle. One degree is represented as 1⁰.

E.g. – sin90⁰=1

Another is “R” or “RAD”; it means the current angle mode is in Radian. A radian had to deal with pi). This is a short cut symbol; π numerically means 3.14 or 22/7. Measurements of angles using radian are called the “radian system of angular measurements.” It is 1/2πr of the circumference of a circle.

E.g. – sin (π/2) =1

The last one is “G” or “GRA”; it means the current angle mode is in Grad. A grad is 1/400 of the circumference of a circle.

E.g. – sin 100 grads= cos 400 grads =1

Degree is the default angle mode on a programmable/scientific calculator. If there is a degree sign after the angle, the trig function evaluates its parameter as a degree measurement, if not, the trig function evaluates it parameter as a radian measurement because radian measurements are considered to be “natural” measurements for angles.

All these three modes are basically used to find angles, especially when doing trigonometry. 

The applicability of the commutative, associative and distributive laws

Commutative law is used while adding or multiplying. With this law the numbers or letters switch positions and the answer remains the same.

Example:   a + b = b + a

6 × 3 = 3 × 6

Associative law is also used while adding, or multiplying. Its  the same procedure as the commutative law, at the end you will remain with the same answer.

Example: (GF + DA) + WE = GF + (DA + WE)

25 × (12 × 3) = (25× 12) × 3

(6 + 3) + 4 = 9 + 4 = 13

(5 × 3) × 8 = 15 × 8 = 120

Distributive law is used while multiplying mostly.  It’s the best one to use, but you have to pay keen attention the way you distribute the numbers and letters. This is because there are positive (+) and negative (-) numbers.  These two signs will determine if the answer is correct or incorrect.

Example:   a × (b + c) = a × b + a × c

3 × (5 + 9) = 3 × 5 + 3 × 9

7 × (7 – 5) = 7 × 7 – 7 × 5

It does not matter the way you work out the equation as long as the answers are the same as well as the sign. You will get the same answer when you multiply a number by a group of numbers added together, or do each multiply separately then add them.

But the commutative and distributive laws cannot be divided while the associative law cannot be subtracted.

Relevance oof series and sequence in everyday life

     Series and sequence are relevance to every day in a sense that it becomes a routine. For series and sequence, they can be fine or infinite. The two examples below are both finite and infinite in some cases. Going to school is finite but the daily route is infinite once a person has life.

     The meaning of series is a group or number of akin things while sequence is the order in which things follow, regular or continuous. These two mathematical topic helps in everyday life because of its route. For instance the school program, students as well has teachers have to be at school at a specific time five of days week. The daily routine, is to have eight periods of classes everyday also break and lunch at a set/specific. This can be related to series and sequence, it occurs each day, one day after the other.

    Another example may include what a person does each morning after waking up. These are a few steps to follow or a person may use in the mornings:

1. make the bed
2. brush your teeth
3. doing chores
4. take a bathe
5. make breakfast
6. clean the dishes after breakfast
7. leave the house

This is a basic routine to follow each morning, also can be considered as proper hygiene.

      Mathematically series and sequence has to deal with numbers/letters ect. This is a short information about series and sequence that was given to us (mathematics students) in class from Mr. Chambers, this information was taken from the Pure Mathematics for Cape, vol 1. “For a finite series or sequence the number of terms are usually denoted by n, and for all series and sequence the general or (r^th) term (a_n) or (u_r). The first term a₁ is often denoted by (a) the sum of the first (n) terms of a series is denoted by (S_n), this is known as the partial sum. ”

“Depending on the pattern the series or sequence follows, the general terms can usually be found either from its position in the series or sequence or form the term/terms that precede it. E.g. Fibonacci sequence: 1,1,2,3,5,8,13,21… each term is found by adding the two proceeding terms U_r= U_r-2,U_r-1. This is normally called recurrence relation.”