Trigonometry

#	📌 Category	📝 Formula / Definition
1	🔺 Trigonometric Ratios (In a right-angled triangle OAB with angle θ)	sin θ = $\dfrac{\text{Perpendicular}}{\text{Hypotenuse}} = \dfrac{AB}{OB}$ cos θ = $\dfrac{\text{Base}}{\text{Hypotenuse}} = \dfrac{OA}{OB}$ tan θ = $\dfrac{\text{Perpendicular}}{\text{Base}} = \dfrac{AB}{OA}$
2	🔄 Inverse Trigonometric Ratios	cosec θ = $\dfrac{1}{\text{sin } \theta} = \dfrac{\text{Hypotenuse}}{\text{Perpendicular}}$ sec θ = $\dfrac{1}{\text{cos } \theta} = \dfrac{\text{Hypotenuse}}{\text{Base}}$ cot θ = $\dfrac{1}{\text{tan } \theta} = \dfrac{\text{Base}}{\text{Perpendicular}}$
3	🧮 Trigonometrical Identities	1. $\sin^2 \theta + \cos^2 \theta = 1$ 2. $1 + \tan^2 \theta = \sec^2 \theta$ 3. $1 + \cot^2 \theta = \text{cosec}^2 \theta$
4	📈 Angle of Elevation	When looking up at an object placed above eye level, the angle between the horizontal line of sight and the upward line of sight is the angle of elevation.
5	📉 Angle of Depression	When looking down at an object placed below eye level, the angle between the horizontal line of sight and the downward line of sight is the angle of depression.

Angle (θ)	0°	30° (π/6)	45° (π/4)	60° (π/3)	90° (π/2)
sin θ	0	$\dfrac{1}{2}$	$\dfrac{1}{\sqrt{2}}$	$\dfrac{\sqrt{3}}{2}$	1
cos θ	1	$\dfrac{\sqrt{3}}{2}$	$\dfrac{1}{\sqrt{2}}$	$\dfrac{1}{2}$	0
tan θ	0	$\dfrac{1}{\sqrt{3}}$	1	$\sqrt{3}$	Not defined

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