# Topics Home The identify $\cos^2 \theta + \sin^2 \theta = 1$ is required for finding trigonometric ratios. Example 1 Find exactly the possible values of $\cos \theta$ for $\sin \theta = \dfrac{5}{8}$. Show Solution \begin{align} \displaystyle \cos^2 \theta + \sin^2 \theta &= 1 \\ \cos^2 \theta + \sin^2 \dfrac{5}{8} &= 1 \\ \cos^2 \theta + [...] # Trigonometric Ratios Home Circles with Cnetre (0,0) Consider a circle with centre (0,0) and radius r units. Suppose (x,y) is any point on this circle. Using ths distance formula; \( \begin{align} \displaystyle \sqrt{(x-0)^2+(y-0)^2} &= r \\ \therefore x^2+y^2 &= r^2 \end{align} $x^2+y^2 = r^2$ is the equation of a circle with centre $(0,0)$ and radius $r$. [...] # Degree-Radian Conversions

Home 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, $1''$, as $\dfrac{1}{60}$ of [...] # Volumes for Two Functions

Home If the region bounded by the upper function $y_{upper}=f(x)$ and the lower funciton $y_{lower}=g(x)$, and the lines $x=a$ and $x=b$ is revolved about the $x$-axis, then its volume of revolution is given by: \begin{align} \displaystyle V &= \int_{a}^{b}{\Big([f(x)]^2 - [g(x)]^2\Big)}dx \\ &= \int_{a}^{b}{\Big(y_{upper}^2 - y_{lower}^2\Big)}dx \end{align} Example 1 Find the volume of [...] 