trigonometry sum no. 1

EXAMPLE 1 :
Given tanA = 4/3, find the other trigonometric ratios of the angle A.
Solution :
trigonometry diagram no. 1
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.