Question

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

spam=20 ans reported​

Answer 1

We will use the basic formula of sine, cosine, and tangent functions to solve the question.

Let's draw a figure according to the given question.

[ Note : refer to the attachment for the figure ]

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

Given that:

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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