Arc Length and Sector Area

You should know with these terms relating to the parts of a circle. The centre of a circle is the point which is equidistant from all points on the circle. A radius of a circle a straight line joining the centre of a circle to any point on the circumference. A minor arc is an […]

Degree Measurement of Angles One full revolution makes an angle of $360^{\circ}$, and the angle on a straight line is $180^{\circ}$. Therefore, one degree, $1^{\circ}$, can be defined as $\dfrac{1}{360}$ of one full revolution. For greater accuracy we define one minute, $1’$, as $\dfrac{1}{60}$ of one degree and one second, $1^{\prime \prime}$, as $\dfrac{1}{60}$ of […]
Trigonometric properties such as the sum of squares of sine and cosine with the same angle is one, $$\displaystyle \sin^2{\theta} + \cos^2{\theta} = 1 \\ \cos\Big(\frac{\pi}{2} – \theta \Big) = \sin{\theta}$$ can simplify harder integration. Worked Example of Integration using Trigonometric Properties (a)   Find $a$ and $b$ for \(\displaystyle \frac{1}{x(4-x)} = \frac{a}{x} […]
There are many areas to apply the compound angle formulas, and trigonometric proof using the compound angle formula is one of them.  \begin{aligned} \require{color}\sin (x + y) &= \sin x \cos y + \sin y \cos x &\color{green} (1) \\\sin (x – y) &= \sin x \cos y – \sin y \cos x &\color{green} […]