Below you can find the graphic drawings of 2 over sinx, 3 over sinx and 4 over sinx. We wish everyone a good work...
$(sin(x))^2$ graph:
$(sin(x))^3$ graph:
$(sin(x))^4$ graph:
Thursday, August 31, 2023
Perimeter and Area Formulas of Geometric Shapes | All Geometry Formuls
You can find the perimeter and area formulas of all geometric shapes from the image below. We wish everyone a good work...
Rectangle perimeter = 2(a+b)
Rectangle area = a.b
Square perimeter = 4a
Square area = $a^2$
Triangle perimeter = a+b+c=2s
Triangle area = 1:1/2*b*h & 2: $\sqrt{s(s-a).(s-b).(s-c)}$
Right triangle perimeter = b+h+d
Right triangle area = 1/2 bh
Equilateral triangle perimeter = 3a
Equilateral triangle area = 1: 1/2 a.h & 2: $\frac{\sqrt{3}}{4}.a^2$
Isosceles right triangle perimeter = 2a+d
Isosceles right triangle area = 1/2 a^2
Parallelogram perimeter = 2(a+b)
Parallelogram area = a.h
Rhombus perimeter = 4a
Rhombus area = 1/2 d1 d2
Trapezium perimeter = Sum of its four sides
Trapezium area = 1/2 h(a+b)
Circle perimeter = 2πr
Circle area = πr^2
Semicircle perimeter = πr+2r
Semicircle area = 1/2πr^2
Ring (shaded region) perimeter = -
Ring (shaded region) area = π(R^2-r^2)
Sector of a circle perimeter = I + 2r where I = (Ɵ / 360) * 2πr
Sector of a circle area = Ɵ/360 * πr^2
Wednesday, August 30, 2023
Graph of tanhx^-1 | What is tanh^-1x graph drawing?
The graph of tanhx to the -1 is as follows.
$tanhx^{-1}$ graph:
 |
| tanh^-1x graph |
Graph of cothx^-1 | What is coth^-1x graph drawing?
The graph of cothx to the -1 is as follows.
$cothx^{-1}$ graph:
 |
| cothx^-1 graphic |
Graph of coshx^-1 | What is cosh^-1x graph drawing?
The graph of coshx to the -1 is as follows.
$coshx^{-1}$ graph:
 |
| cosh^-1(x) graph |
Graph of sinhx^-1 | What is sinh^-1x graph drawing?
The graph of sinhx to the -1 is as follows.
$sinhx^{-1}$ graph:
 |
| sinh^-1x graph |
Tuesday, August 29, 2023
Special Power Series | ex | sinx | cosx | tanx | ln(1+x) | sinhx | coshx | tanhx | sinh^-1 | tanh^-1 All Series
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categories: all special power series, coshx series, ex series, sinh-1 series, sinhx series, sinx series
categories: all special power series, coshx series, ex series, sinh-1 series, sinhx series, sinx series
You can reach all special power series formulas from below. We wish you all good lessons...
sinx series:
$sin^{-1}x$ series:
$e^x$ series:
(all x)
(all x)
cosx series:
(all x)
tanx series:
(|x| < π/2)
(|x|<1)
$sinh^{-1}x$ series:
$tan^{-1}x$ series:
(|x|<1)
ln(1+x) series:
(-1<x≤1)
sinhx series:
(all x)
coshx series:
(all x)
tanhx series:
(|x|<π/2)
(|x|<1)
$tanh^{-1}x$ series:
(|x|<1)
Maclaurin Series Formula | What is the Maclaurin series?
If the series is zero-centered (a=0), the Taylor series takes a simpler form and this special series is called the Maclaurin series after the Scottish mathematician Colin Maclaurin.
Maclaurin Series Formula:
Monday, August 28, 2023
Epicycloid Definition | Epicycloid Parametric Equations
This is the curve described by a point P on a circle of radius b as it rolls on the outside of a circle of radius a. The cardioid is a special case of an epicycloid.
Z Transforms | All Function and Transform
You can find all the Z transforms below. We wish you good work...
provided f(∞) exists.
Shift Theorem
Initial value theorem
Final value theorem
Inverse Formula
Sunday, August 27, 2023
Mechanics Kinematics & Centres of Mass Definitions and Formulas
Kinematics:
Motion constant acceleration
$v=u+ft$
$s=ut+\frac{1}{2}ft^2=\frac{1}{2}(u+v)t$
$v^2=u^2+2f.s$
General solution of $\frac{d^2x}{dt^2}=-w^2x$ is
x=a.coswt + b.sinwt = R.sin(wt+φ)
where $R=\sqrt{a^2+b^2}$ and cosφ = a / R, sinφ = b / R.
In polar coordinates the celocity is 
and the acceleration is
and the acceleration is
Centres of mass:
The following results are for uniform bodies:
- hemispherical shell, radius r ⇾ $\frac{1}{2}r$ ⇾ from centre
- hemisphere, radius r ⇾ $\frac{3}{8}r$ ⇾ from centre
- right circular cone, height h ⇾ $\frac{3}{4}h$ ⇾ from vertex
- arc, radius r and angle 2θ ⇾ (r sinθ) / θ ⇾ from centre
- sector, radius r and angle 2θ ⇾ ($\frac{2}{3}r$ sinθ) / θ ⇾ from centre
Chebyshev Polynomials
You can find the Chebyshev polynomials below. We wish everyone a good lesson...
Leibnitz's Theorem | Leibnitz Derivative Rule
You can find the Leibnitz derivative theorem below. We wish you good lessons...
Product Rule & Quotient Rule & Chain Rule (Derivative)
You can find the product rule, quotient rule and chain rule in the derivative below. We wish you good lessons.
Product Rule:
$\frac{d}{dx}(u(x).v(x))=u(x)\frac{dv}{dx}+v(x)\frac{du}{dx}$
Quotient Rule:
$\frac{d}{dx}(\frac{u(x)}{v(x)})=\frac{v(x)\frac{du}{dx}-u(x)\frac{dv}{dx}}{[v(x)]^2}$
Chain Rule:
$\frac{d}{dx}(f(g(x)))=f'(g(x))×g'(x)$
Tuesday, August 22, 2023
Laplace Transforms | Function and Transform (Examples)
You can find Laplace transforms below. We wish everyone good work.
You can find sample solutions below.
Sunday, August 20, 2023
General Rules of Differantiation
In the following, u, v, w are functions of x; a, b, c, n are constants [restricted if indicated]; e=2.71828... is the natural base of logarithms; In u is the natural loraithm of u [i.e. the loraithm to the base e] where it is assumed thad u>0 and all angles are in radians.
Graphs of Hyperbolic Functions (Sinhx, Coshx, Tanhx, Cothx Graphics)
y=sinh x graph:
y=cosh x graph:
y=tanh x graph:
y=coth x graph:
y=sech x graph:
y=csch x graph:
Expression of Hyperbolic Functions In Terms of Others (Table)
In the following we assume x>0.
