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In Trigonometry, the 6 trigonometric functions which are, sine, cosine, tangent, cosecant, secant and cotangent of an angle play a very important role. All the concepts of Trigonometry are based on these functions and they help us evaluate the values of the sides and angles of triangles and other geometric structures. There are formulas, identities and problems based on the relationship of these functions and therefore in order to get the answer, we have to use them appropriately.
Example 1: A 5m long ladder leans against a wall with the base of the ladder being 4m away from the base of the wall. What is the approximate angle made by the ladder with respect to the ground?
Based on the question, here is the diagram.
Let the angle made by the ladder with respect to the ground = θ
The trigonometric function, cos(θ) = (adjacent side)/ (hypotenuse)
Therefore, cos(θ) = 4m/5m
This gives: cos(θ) = 4/5-> θ = cos-1(4/5)
This implies: θ = 36.87°
Therefore the angle made by the ladder with the ground = 36.87°.
Example 2: Prove the given trigonometric identity: tan(x) + cot(x) = 1/ [(sin(x) * cos(x)].
Here let’s start with the left-hand side of the equation -> tan(x) + cot(x)
We can also write the above expression as: tan(x) + cot(x) = [sin(x/cos(x)] + [cos(x)/sin(x)]
Here we can take a common denominator and this gives: [sin2(x) + cos2(x)]/ [(sin(x) * cos(x)]
According to the trigonometric identity, sin2(x) + cos2(x) = 1.
Hence we get: 1/ [(sin(x) * cos(x)] = right-hand side of the equation!
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