trigonometry sum no. 1

EXAMPLE 1 :

Given tanA = 4/3, find the other trigonometric ratios of the angle A.

Solution :

Fig. 8.8

Let us first draw a right Δ ABC (see Fig 8.8).

Now, we know that tan A = BC/AB = 4/3

Therefore, if BC = 4k, then AB = 3k, where k is a positive number.

Now, by using the Pythagoras Theorem, we have

AC² = AB² + BC² = (4k)² + (3k)² = 25k²

So, AC = 5k

Now, we can write all the trigonometric ratios using their definitions.

sin A = BC/AC = 4k/5k = 4/5

cos A = AB/AC = 3k/5k = 3/5

Therefore, cot A = 1/tan A = 3/4, cosec A = 1/sin A = 5/4 and sec A = 1/cos A = 5/3.