A dark spacetime grid stretches silently across a cosmic void. As a glowing sphere glides through it, the grid bends and ripples around its path, visualizing the curvature of spacetime from Einstein’s General Relativity. Subtle 3D rotation and faint starlight enhance the scene’s depth, revealing gravity as the graceful warping of the universe’s fabric.
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
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…
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.
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 𝛑 r Hence, L = ( \dfrac { \mathrm{θ_{deg} } } {360} ) × 2 𝛑 r …
Radians
Radian is the SI unit to measure the angle subtended by an arc of a circle. It is the measurement of the angle subtended by an arc of a circle whose length is equal to the radius of the circle. θ (in radians) = \( \dfrac { \mathrm{length \ \ of \ \ arc} } {…
Odd numbers
A number not divisible by 2 is called an odd number. Any number whose unit digit(last digit) is either 1,3,5,7 or 9 is an odd number. The set of all odd numbers is represented as Odd numbers = { 2n+1: n ∈ Z } where Z is the set of all integers. When an even…
Even Numbers
A number divisible by 2 is called an even number. All numbers whose unit digit(last digit) is either 0,2,4,6 or 8 is an even numbers. The set of all even numbers is represented as follows: Even numbers = { 2n: n ∈ Z } where Z is the set of all integers. Zero is…