# Blog # Derivative of sin x by First Principles

Method 1 Required Trigonometric Formula $\displaystyle \sin A-\sin B = 2 \cos \left( \frac{A+B}{2} \right) \sin \left( \frac{A-B}{2} \right)$ \( \require{ASMsymbols} \displaystyle \begin{align} \frac{d}{dx} \sin x &= \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h} \\ &= \lim_{h \to 0} \frac{2 \cos \left(x+\frac{h}{2} \right) \sin \frac{h}{2}}{h} &\color{green}{\text{by the given formula above}} \\ &= \lim_{u \to […]

# Interactive Video – Velocity-Time Graphs: Straight Lines # How to Find the Centre, Period, Velocity, Acceleration and Times of Simple Harmonic Motion Explained

Simple Harmonic Motion is a specific type of periodic motion where is any motion whose displacement-time equation, apart from the constants, is a single sine and/or cosine function. Of particular importance is a certain kind of rectilinear motion known as Simple Harmonic Motion. A particle is said to be undergoing in simple harmonic motion with […] # How to Find the Number of Roots by Stationary Points and Deduce for an Inverse Function Explained Quickly

The stationary points can be found by solving the derivatives to zero. Some cubic equations have one root if the stationary points are in the same sign, such as two stationary points are either above the x-axis or below the x-axis. In these cases, the cubic graph cuts the x-axis only once, so the cubic […] # The Trajectory of Projectile Motion on an Inclined Plane with Maximum Range Explained

Projectile motion on an inclined plane is one variation of projectile motion and the trajectory can be used to determine the position of the landing object on the included plane. We will discuss; path of the trajectory of the projectile range of the projectile maximum range initial direction is perpendicular to the direction at which […] # AREA of the Shapes Formula Explained with Clear Examples and 9 Comprehensive Video Lessons

What is the Area of the Shapes? A shape is defined as the figure surrounded by the closed boundary in geometry. The closed boundary consists of lines, curves and points. The amount of space inside the boundary that expresses the extent of a two-dimensional shape is defined as an area. The area is measured in […] # Read This Simple Work for Definite Integrals by U-SUBSTITUTION Method Explained in 3 Distinct Examples and Video Lessons

U-substitution in definite integrals is very similar to the method in indefinite integrals, while the initial bounds (usually x-values) need to be changed to the corresponding u-values for upper and lower limits. You need to account for the limits of the integration. Alternatively, you can integrate the integral expressions using u-substitutions, then change u-expressions back […]