A Visual to Trigonometry

Instructions

Trigonometry is often viewed as a hard and weird field of mathematics. It is not very clear how trigonometric ratios can be used and what they actually mean. Here is a very beautiful visual intuition to the six trig ratios and how they play out as θ (the angle) changes. Let the base, perpendicular and hypotenuse of a right angled triangle be b, p and h respectively. If you know basic trigonometry, as in sin (θ) = p/h cosec (θ) or csc (θ) = h/p = 1/(sin (θ)) cos (θ) = b/h sec (θ) = h/b = 1/(cos (θ)) tan (θ) = p/b cot (θ) = b/p = 1/(tan (θ)) you can try and construct this diagram for yourself and see why these side lengths can be written as ratios. If you look at this diagram and think for a while, it is possible to prove the three fundamental trig square ratios as well, by applying the Pythagorean theorem in 3 right triangles! sin² (θ) + cos² (θ) = 1 1 + cot² (θ) = csc² (θ) 1 + tan² (θ) = sec² (θ) It also gives a visual intuition to why cos (θ) or cosine (θ) is actually the 'co' to sine (θ), cosec (θ) is 'co' to sec (θ) and, cotangent (θ) in 'co' to tangent (θ). You also see why cotangent and tangent are called such, it is actually tangent to the circle! It would be more accurate that in the diagram all the ratios were written as a product of the ratio and the radius, as in r × sin (θ), etc. But as the radius = 1 unit, the ratios can be written on their own. #trignometry #trig #ratios #trigonometry #math #maths