# Math Formulas

### General | Latest Info

Math formulas, for all concepts covered under different classes, as per CBSE Syllabus, are provided here by our expert teachers. To solve mathematical problems easily, students should learn and remember basic formulas based on certain fundamentals such as Algebra, arithmetic, and Geometry. Also, check with Maths Syllabus here for all classes. Addition, subtraction, multiplication and division are easy, what if you come across derivation, calculus and Geometry? You would need formulas to solve them. Here, at BYJUS, you get a unique way of solving math problems which will make you learn how equations come into existence, which is way better than memorizing and applying formula. We present you a host of formulas for your reference to solve all important mathematical operations and questions. Also, each formula here is given with solved examples.

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### Trigonometry

Word Trigonometry comes from the Greek words trigonon and metron. Until about the 16th century, Trigonometry was chiefly concerned with computing numerical values of missing parts of triangle when values of other parts were give. For example, if the lengths of two sides of a triangle and the measure of enclose angle are know, third side and two remaining angles can be calculate. Such calculations distinguish Trigonometry from geometry, which mainly investigates qualitative relations. Of course, this distinction is not always absolute: Pythagorean theorem, for example, is a statement about the lengths of three sides in right triangle and is thus quantitative in nature. Still, in its original form, Trigonometry was by and large an offspring of geometry; it was not until the 16th century that the two became separate branches of mathematics.

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### Other Tips

{matheq}A=\frac{\sqrt{3}s^2}{{4}}{endmatheq} regular area of triangle formula is provided on the SAT reference sheet, but it requires that you know the height of the triangle. Sometimes you arent give height and you need to calculate it, but you can quickly find the area of an equilateral triangle by plugging the length of one of its sides into the formula above. No need to calculate height! {matheq}(x-h)^2+(y-k)^2=r^2{endmatheq} there is usually one question involving the equation of circle. In this equation, {matheq}(h,k){endmatheq} is coordinate For center of circle, and {matheq}r{endmatheq} is the radius of the circle. Some students get nervous when they hear that trig is on the SAT, but it most often appears in the form of trig ratios. Remember that For give angle in right triangle, value of sine is length of opposite side divided by length of hypotenuse, or opposite / hypotenuse. Just like with sine, remember what cosine ratio is: length of adjacent side divided by length of hypotenuse, or adjacent / hypotenuse. Last but not least, tangent ratio is length of opposite side divided by length of adjacent side, or opposite / adjacent. Some students find mnemonic SOH CAH TOA helpful for remembering trig ratios. While the most common form of trig is basic ratios, you may encounter things like unit circle or more Advanced Math. If you need to convert degrees to radians, multiply degrees by {matheq}\frac{\pi}{180}{endmatheq} if you need to convert radians to degrees, multiply radians by {matheq}\frac{180}{\pi}{endmatheq} {matheq}a^2+b^2=c^2{endmatheq} Pythagorean Theorem applies to right triangles, and allows you to solve For one of side lengths give any other side length. {matheq}a{endmatheq} and {matheq}b{endmatheq} are legs of triangle, and {matheq}c{endmatheq} is hypotenuse. {matheq}(x-h)^2+(y-k)^2=r^2{endmatheq} sit will probably involve one question with a regular polygon that isn't triangle or square. Regular polygons have unique and consistent properties based on their number of sides, and knowing these properties can help you solve these problems. This equation tells you what degree measure at each angle is based on the number of sides. {matheq}(x-h)^2+(y-k)^2=r^2{endmatheq} sit provides you with two special right triangles you may already be familiar with on your reference sheet 30 - 60 - 90 and 45 - 45 - 90 triangles. However, 3 - 45 is a special right triangle with sides that are straightforward integers. This triangle is often incorporated into SAT problems, especially the no - calculator portion, so be on the lookout for it! It can save you from having to use the Pythagorean Theorem. Another special right triangle with whole - number sides, 5 - 12 - 13 triangle, is less known and shows up less often than 3 - 45. Still, it helps to be able to quickly solve remaining sides without the Pythagorean Theorem, so check for these numbers or their multiples in triangle problems. {matheq}(x-h)^2+(y-k)^2=r^2{endmatheq} although geometry questions don't make up a huge portion of SAT, you may still find questions either about arcs or sectors in circle.

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### The Standard Model

Standard Model of physics as table. Shutterstock Standard Model of particle physics is often visualized as a table, similar to a periodic table of elements, and used to describe particle properties, such as mass, charge and spin. The table is also organized to represent how these teeny, tiny bits of matter interact with fundamental forces of nature. The Grand theory of almost everything actually represents a collection of several mathematical models that prove to be timeless interpretations of laws of physics. Here is a brief tour of topics covered in this gargantuan equation. Almost half of this equation is dedicated to explaining interactions between bosons, particularly W and Z bosons. Bosons are force - carrying particles, and there are four species of bosons that interact with other particles using three fundamental forces. Photons carry electromagnetism, gluons carry strong force and W and Z bosons carry weak force. The most recently discovered boson, Higgs boson, is a bit different; its interactions appear in the next part of the equation. This part of the equation describes how elementary matter particles interact with weak force. According to this formulation, matter particles come in three generations, each with different masses. Weak force helps massive matter particles decay into less massive matter particles. This section also includes basic interactions with the Higgs field, from which some elementary particles receive their mass. Intriguingly, this part of the equation makes assumptions that contradict discoveries made by physicists in recent years. It incorrectly assumes that particles called neutrinos have no mass. This last part of the equation includes more ghosts. These ones are called Faddeev - Popov ghosts, and they cancel out redundancies that occur in interactions through weak force.

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### Calculus

In this case, we have a sum and difference of four terms and so we will differentiate each of the terms using first property from above and then put them back together with proper sign. Also, for each term with multiplicative constant, remember that all we need to do is factor constant out and then do derivative.S Notice that in the third term exponent was one and so upon subtracting 1 from the original exponent we get a new exponent of zero. Now recall that {matheq}{x^0} = 1{endmatheq} don't forget to do any basic arithmetic that needs to be done, such as any multiplication and / or division in coefficients. The point of this problem is to make sure that you deal with negative exponents correctly. Here is derivative. Make sure that you correctly deal with exponents in these cases, especially negative exponents. It is an easy mistake to go the other way when subtracting one off from negative exponent and get {matheq} - 6{t^{ - 5}}{endmatheq} instead of correcting {matheq} - 6{t^{ - 7}}{endmatheq} now in this function second term is not correctly set up for us to use Power Rule. The Power Rule requires that term be variable to Power only and term must be in numerator. So, prior to differentiating, we first need to rewrite the second term into form that we can deal with. Note that we leave 3 in the denominator and only move variable up to the numerator. Remember that the only thing that gets an exponent is the term that is immediately to the left of the exponent. If wed wants three to come up as well, wed have write, {matheq}\frac{1}{{{{\left( {3z} \right)}^5}}}{endmatheq} so be careful with this! It's very common mistake to bring 3 up into the numerator as well at this stage. Now that we 've got functions rewritten into proper form that allows us to use Power Rule, we can differentiate function. Here is derivative of this part. {matheq}y' = 24{z^2} + \frac{5}{3}{z^{ - 6}} + 1{endmatheq} all of the terms in this function have root in them. In order to use Power Rule, we need to first convert all roots to fractional exponents. Again, remember that the Power Rule requires us to have a variable number and that it must be in numerator of term. Here is the function written in proper form. In the last two terms, we combine exponents. You should always do this with this kind of term. In later section we will learn of technique that would allow us to differentiate this term without combining exponents,. However, it will take significantly more work to do. Also, do forget to move terms in denominator of third term up to numerator. We can now differentiate function. Make sure that you can deal with fractional exponents. You will see a lot of them in this class.

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### Pythagorean theorem

Use the Pythagorean Theorem to find the unknown side of the right Triangle. A long time ago, Greek mathematician named Pythagoras discovered an interesting property about right triangles: sum of squares of lengths of each triangleas legs is same as the square of length of triangleas hypotenuse. This propertyawhich has many applications in science, art, engineering, and architectural now called Pythagorean Theorem. Please take a look at how this theorem can help you learn more about the construction of triangles. And the best partayou is that do even have to speak Greek to apply Pythagorasa discovery. Pythagoras studied right triangles, and relationships between legs and hypotenuse of right triangle, before deriving his theory. In box above, you may have noticed words asquare, as well as small 2s on top right of letters To square number means to multiply it by itself. So, for example, to square number 5 you multiply 5 5, and to square number 12, you multiply 12 12. Some common squares are shown in table below. When you see equation, you can think of this as the length of side times itself, plus the length of side B times itself is same as the length of side c times itself. Letas try out all of the Pythagorean Theorems with the actual right Triangle. This theorem holds true for this right triangleathe sum of squares of lengths of both legs is same as the square of length of hypotenuse. And, in fact, it holds true for all right triangles. The Pythagorean Theorem can also be represented in terms of area. In any right Triangle, area of square drawn from hypotenuse is equal to the sum of areas of squares that are drawn from two legs. You can see this illustrated below in same 3 - 45 right Triangle. Note that the Pythagorean Theorem only works with right triangles. You can Use Pythagorean Theorem to Find length of hypotenuse of right Triangle If you know the length of triangleas other two sides, call legs. Put another way, if you know the lengths of and B, you can find c. In Triangle above, you are given measures for legs and B: 5 and 12, respectively. You can use the Pythagorean Theorem to find value for length of c, hypotenuse. Using formula, you find that the length of c, hypotenuse, is 13. In this case, you do not know the value of c ayou were given square of length of hypotenuse, and had to figure it out from there. When you are given an equation like and are asked to find the value of c, this is called finding the square root of a number.

* Please keep in mind that all text is machine-generated, we do not bear any responsibility, and you should always get advice from professionals before taking any actions.

###### * Please keep in mind that all text is machine-generated, we do not bear any responsibility, and you should always get advice from professionals before taking any actions

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