SOLUTION
Step 1: Definition of Trigonometry
Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle. In trigonometry, the angles can be either measured in degrees or radians. Some of the most commonly used trigonometric angles for calculations are 0°, 30°, 45°, 60° and 90°.
Step 2: State the three trigonometric ratios
The trigonometric ratios of a triangle are also called the trigonometric functions. Sine, cosine, and tangent are 3 important trigonometric functions and are abbreviated as sin, cos and tan.
Step 3: Show how these ratios or functions, evaluated in case of a right-angled triangle.
Consider the right-angled triangle above, where the longest side is called the hypotenuse, and the sides opposite to the hypotenuse are referred to as the adjacent and opposite sides.
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}[/tex]STEP 4: Evaluate the other 3 ratios that can be derived from the given ratios in step 3
[tex]\begin{gathered} co\sec \theta=\frac{1}{\sin \theta}=\frac{1}{\frac{\text{opposite}}{\text{hypotenuse}}}=\frac{\text{hypotenuse}}{\text{opposite}} \\ \sec \theta=\frac{1}{\cos \theta}=\frac{1}{\frac{\text{adjacent}}{\text{hypotenuse}}}=\frac{\text{hypotenuse}}{\text{adjacent}} \\ \cot \theta=\frac{1}{\tan \theta}=\frac{1}{\frac{\text{opposite}}{\text{adjacent}}}=\frac{\text{adjacent}}{\text{opposite}} \end{gathered}[/tex]Knowing .these ratios are the basic concepts of Trigonometry.
