Snippets

math

What are 'radia...

What are 'radians' ? One radian is the angle of an arc created by wrapping the radius of a circle around its circumference. In this diagram, the radius has been wrapped around the circumference to create an angle of 1 radian. The pink lines show the radius being moved from the inside of the circle to the outside: [nameofpicture.svg] The radius $$r$$ fits around the circumference of a circle exactly 2p times. That is why the circumference of a circle is given by: $$circumference = 2 \pi r$$

math

Converting radi...

Converting radians to degrees: To convert radians to degrees, we make use of the fact that $$\pi$$ radians equals one half circle, or 180º. This means that if we divide radians by $$\pi$$, the answer is the number of half circles. Multiplying this by 180º will tell us the answer in degrees. So, to convert radians to degrees, multiply by $$\frac{180}{\pi}$$, like this: $$ degrees = radians \times \frac{180}{\pi}$$

math

Converting degr...

Converting degrees to radians: To convert degrees to radians, first find the number of half circles in the answer by dividing by 180º. But each half circle equals $$\pi$$ radians, so multiply the number of half circles by $$\pi$$. So, to convert degrees to radians, multiply by $$\frac{\pi}{180}$$, like this: $$ radians = degrees \times \frac{\pi}{180}$$

math

Solution of qua...

Solution of quadratic equations. A quadratic equation is any equation having the form \(ax^2+bx+c=0\) where \(x\) represents an unknown, and \(a,b\) and \(c\) represent known numbers such that \(a\) is not equal to 0. There are two stages in solving quadratic equations. 1) Find discriminant using formula \(D=b^2-4ac\)
2) Check the sign of discriminant: 2.1) If \(D>0\), then equation has two (unequal) real solutions \(x_{1,2}=\dfrac{-b\pm\sqrt{D}}{2\cdot a}\)
2.2) If \(D=0\), then equation has two (equal) real solutions \(x=\dfrac{-b}{2\cdot a}\)
2.3) If \(D<0\), then equation has no real solutions.

Loading rules...