MATHEMATICS
Resources & Insights
Explore mathematics, the foundational science of numbers, patterns, and logical reasoning. Learn key topics including algebra, geometry, calculus, statistics, and number theory. Ideal for students, educators, and enthusiasts seeking to develop problem-solving skills and apply mathematical concepts in science, technology, finance, and everyday life.
cscθ (Cosecant of an angle)
secθ (Secant of an angle)
cotθ (Cotangent of an angle)
tanθ (Tangent of an angle)
Pythagoras’ theorem
Pythagoras’ theorem is stated as : The sum of the areas of the two squares on the perpendicular(p) and base(b) of a right-angle triangle is equal to the area of the square on the hypotenuse(h). i.e. p2 + b2 = h2 READ MORE...
Sides of a Triangle
A right-angle triangle is a triangle in which one of the angles measures 90°. Right-angled triangles have wide applications in mathematics and physics and as such, it became convenient to have specific names for their sides so that the problem statement in mathematics can be easily described. One of the angles measures 90°. If we denote one of the remaining two angles by θ, then the third angle would be 90°- θ. With reference to the angle θ, we have the below definitions: The side opposite the right angle(90°) is called the hypotenuse. The hypotenuse is also the longest side in a right-angle triangle. The side opposite to the angle θ is called perpendicular. The side containing both the right angle and θ […] READ MORE...
Trigonometric functions in terms of a unit circle context
The trigonometric functions can be described on an x-y coordinate plane (Euclidean plane) using a circle of radius 1 unit and cutting a sector that subtends an angle θ at the centre. Refer to the diagram below for details. READ MORE...
Relation between radian and degree
By definition, L (length of arc) = ( \dfrac { \mathrm{θ_{deg} } } {360} ) × Circumference (arc length is proportional to angle, one complete arc subtends 360° at center) Also, Circumference = 2 ? r Hence, L = ( \dfrac { \mathrm{θ_{deg} } } {360} ) × 2 ? r - - - - - (i) Now, again by definition, θrad = ( \dfrac{ \mathrm{L} }{ r } ) (radian is ration of arc length to radius) So, L = r × θrad - - - - - (ii) From (i) & (ii), we have r × θrad= ( \dfrac { \mathrm{θ_{deg} } } {360} ) × 2 ? r Or, θrad = θdeg × […] READ MORE...