Understanding Probability and Trigonometry

To all of us students Mathematics has always been a trouble. The huge numbers start encircling the students and to some they also give nightmares.  While some are easily able to solve the concepts, others face trouble in even doing the basics. 

The task that Math takes at hand is to test the intellect and analytical abilities of a student as well as to find out how well he or she is able to retain the concepts. Math problems are just not a matter of books but also find their applications in the real world . 

It is not just about memorizing the  formulae and using these formulae to solve direct questions in your paper. Rather it is much more than that. These formulae and the related concepts that we learn have various practical applications as well. For example: data and charts can be used to solve different problems easily, percentage can be used to calculate a students’ own percentage he has score in his examination and so is the use of average. 

Statistics majorly help seeing the varying trends over time, as well as evaluating on certain other variables, trigonometry has a wide application in the construction sector and so does area and perimeter and other concepts of mensuration. 

Therefore all these concepts of Math have a wide variety of applications. Students have to do a lot in this case and need math assignment help or math homework help if they are trying to work on their own.

Among these concepts are the concepts of probability and trigonometry. These concepts are taught to students at a senior level and require extensive practice. 

The chances or likeability of an event occurring or a proposition being true is what probability talks about and is concerned with. The chances of an event occurring are directly proportional to the probability of the event happening. For example, an unbiased coin is tossed. The two outcomes of this coin are heads and tails and their probability is equal.

Laws of probability:-

  • Mutually exclusive events: In this, the probability of the two events have no outcome in common that is their intersection is zero.
  • Mutually exclusive and exhaustive events: This includes that the probability of events occurring is equal to one.

Terms in probability:-

  1. Conditional probability: The probability of one event occurring such that another event has already occurred and is not equal to zero, is called conditional probability.
  2. Multiplication theorem: If there are two events, then the probability of the occurrence of both the events will be equal to the probabilities having individual identity.
  3. Independent events: The two events are said to be independent when the occurrence of one event has no effect on the occurrence of the other event.
  4. Bayes’ theorem: This theorem is named after the Reverend Thomas Bayes’, which states the probability of an event, on the knowledge of the conditions which is gained by the prior experiments and is associated with the events occurring. 
  5. Random variable: A random variable is also known as discrete variable if it accepts the countably infinite or only finite number of values. For example, the occurrence of head in n tosses of coin. The random variable which accepts the number of values which are non countable is called non discrete or continuous random variable. This helps it to assume values in any particular event. 

Types of probability:-

  1. Theoretical probability: It is based on the chances of an event occurring. It basically involves reasoning behind every probability. For example, if a fair coin is tossed, the theoretical probability of getting any one of them (head or tail) is ½.
  2. Experimental probability: It involves the observation of a particular experiment. The experimental probability is calculated on the number of outcomes which are likely to occur, by the total number of trials done in an experiment. For example, if a coin is tossed 5 times and tails is recorded 2 times, then the experimental probability for tail to occur will be 2/5.
  3. Axiomatic probability: the set of rules or axioms of all types are applied in this probability. The axioms in this probability are set by Kolmogorov’s which are also known as three axioms of Kolmogorov. The chances of the event occurring or non occurring, is quantified by this axiomatic approach. 

Trigonometry is a word in mathematics that helps us to study the different relationships between the angles of triangles and also the side lengths. Trigonometry has different kinds of uses in our daily life. For example, in astronomy it helps us to measure the distance of the star which is near to us and also provides help in the satellite navigation system. In geography, it help in measuring the distance between different landmarks. 

Application of trigonometry:- 

  • It can be used to measure the height of a building or a mountain or any such huge figure.
  • It also finds it application in navigating the directions to place the compass.
  • The entire calculus is based on algebra and trigonometry.
  • It has its applications in physics as well- the sine and cosine functions are used to define the sound and light waves.
  • Maps are created using trigonometry
  • Satellite systems too use this concept
  • Marine biologists too use this concept to calculate the depth to which the sunlight reaches, to study photosynthesis.
  • It also has its applications in in investigating crime scenes especially in cases of accidents. 

Therefore, the immense and wide applications of these concepts make them important chapters to be studied. Also the concepts of probability and trigonometry are a bit difficult thus students may need Math homework help or Math assignment help.

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