3. If sin A = 3/4, Calculate cos A and tan A.

Let us assume a right angled triangle ABC, right angled at B Given: Sin A = 3/4 We know that, Sin function is the equal to the ratio of length of the opposite side to the hypotenuse side. Therefore, Sin A = Opposite side /Hypotenuse= 3/4 Let BC be 3k and AC will be 4k where k is a positive real number. According to the Pythagoras theorem, the squares of the hypotenuse side is equal to the sum of the squares of the other two sides of a right angle triangle and we get, AC2=AB2 + BC2 Substitute the value of AC and BC (4k)2=AB2 + (3k)2 16k2−9k2 =AB2 AB2=7k2 Therefore, AB = √7k Now, we have to find the value of cos A and tan A We know that, Cos (A) = Adjacent side/Hypotenuse Substitute the value of AB and AC and cancel the constant k in both numerator and denominator, we get AB/AC = √7k/4k = √7/4 Therefore, cos (A) = √7/4 tan(A) = Opposite side/Adjacent side Substitute the Value of BC and AB and cancel the constant k in both numerator and denominator, we get, BC/AB = 3k/√7k = 3/√7 Therefore, tan A = 3/√7