Question

If sin A = 3/4



, find the other trigonometric ratios of the angle A.​

Answer 1

I've got the answer as in the image. I hope it helps you.

Answer 2

Answer

3/√7

Step-by-step explanation:

Let ∆ABC be a right-angled triangle, right-angled at point B.

Given

sin A = 3/4

⇒ BC/AC = 3/4

Let BC be 3k. Therefore, hypotenuse AC will be 4k where k is a positive integer.

Applying Pythagoras theorem on ∆ABC, we obtain:

AC2 = AB2 + BC2

AB2 = AC2 - BC2

AB2 = (4k)2 - (3k)2

AB2 = 16k2 - 9k2

AB2 = 7 k2

AB = √7 k

cos A = side adjacent to ∠A / hypotenuse = AB/AC = √7 k / 4k = √7/4

tan A = side opposite to ∠A / side adjacent to ∠A = BC/AB = 3k / √7 k = 3√7

Thus, cos A= √7/4 and tan A = 3/√7

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