Trigonometric ratios:
Let \(ABC\) be a right angled triangle.
Let \(0^\circ < \theta < 90^\circ\).
\(\sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse}} = \frac{AB}{AC}\)
\(\cos \theta = \frac{\text{Adjacent side}}{\text{Hypotenuse}} = \frac{BC}{AC}\)
\(\tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}} = \frac{AB}{BC}\)
\(\text{cosec}\: \theta = \frac{\text{Hypotenuse}}{\text{Opposite side}} = \frac{AC}{AB}\)
\(\sec \theta = \frac{\text{Hypotenuse}}{\text{Adjacent side}} = \frac{AC}{BC}\)
\(\cot \theta = \frac{\text{Adjacent side}}{\text{Opposite side}} = \frac{BC}{AB}\)
\(\tan \theta = \frac{\sin \theta}{\cos \theta}\)
\(\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{1}{\tan \theta}\)
\(\text{cosec}\: \theta = \frac{1}{\sin \theta}\)
\(\sec \theta = \frac{1}{\cos \theta}\)
Trigonometric ratio table:
Angle of elevation:
The angle of elevation is defined as the angle formed by the line of sight and the horizontal line when the point being viewed is above the horizontal level.
That is the case when we raise our heads to look at the object.
Angle of depression:
The angle of depression is defined as the angle formed by the line of sight with the horizontal line when the point being viewed is below the horizontal level.
That is the case when we lower our heads to look at the object.
Important!
The angle of elevation and angle of depression are equal because they are alternate angles.
