Question

If sin A = 3/4 then find the value of cos A, tan A, cot A and Cosec A,​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The value of cos A is $\frac{ \sqrt{7} }{4}$ , value of tan A is $\frac{3}{ \sqrt{7} }$ , value of cot A is $\frac{ \sqrt{7} }{3}$ , value of cosec A is $\frac{4}{3}$

Given : The value of sin A is 3/4

To find : The values of cos A, tan A, cot A, and cosec A

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the required values)

Now, w.r.t an right angled triangle, we can say that :

sinθ = perpendicular/hypotenuse

Here,

sin A = 3/4

Which implies,

• perpendicular = 3
• hypotenuse = 4

Now, applying Pythagoras theorem,

(perpendicular)² + (base)² = (hypotenuse)²

(3)²+(base)² = (4)²

(base)² = 16-9

(base)² = 7

base = √7

In the associated right angled triangle :

• perpendicular = 3
• hypotenuse = 4
• base = √7

Now, we know that

• cos A = base/hypotenuse = $\frac{ \sqrt{7} }{4}$
• tan A = perpendicular/base = $\frac{3}{ \sqrt{7} }$
• cot A = base/perpendicular = $\frac{ \sqrt{7} }{3}$
• cosec A = hypotenuse/perpendicular = $\frac{4}{3}$

(These will be considered as the final result.)

Hence, the value of cos A is $\frac{ \sqrt{7} }{4}$ , the value of tan A is $\frac{3}{ \sqrt{7} }$ , the value of cot A is $\frac{ \sqrt{7} }{3}$ , the value of cosec A is $\frac{4}{3}$