Question

if sin A=¾, calculate cos A and tos A.​

Answer 1

Answer:

so answer this question you see.

Answer 2

Step-by-step explanation:

Given :-

Sin A = 3/4

To find :-

Calculate I) Cos A and ii) Tan A ?

Solution :-

Given that

Sin A = 3/4------------(1)

On squaring both sides then

=> (Sin A )² = (3/4)²

=> Sin² A = (3×3)/(4×4)

=> Sin² A = 9/16

=> 1 - Sin² A = 1 -(9/16)

=> 1 - Sin² A = (16-9)/16

=> 1 - Sin² A = 7/16

We know that

Sin² A + Cos² A = 1

=> Cos² A = 7/16

=> Cos A = ±√(7/16)

=> Cos A = ±√7/4

Since A is acute angle

Cos A = √7/4 --------------(2)

On dividing (1) by (2)

=> (1)÷(2)

=> Sin A / Cos A = (3/4)/(√7/4)

=> Tan A = (3/4)×(4/√7)

=> Tan A = (3×4)/(4×√7)

=> Tan A = 3/√7 or

=> Tan A = (3/√7)×(√7/√7)

=> Tan A = (3×√7)/(√7×√7)

=> Tan A = 3√7/(√7)²

=> Tan A = 3√7/7

Therefore , Tan A = 3/√7 or 3√7/7

Answer:-

The value of Cos A = √7/4

The value if Tan A = 3/√7 or 3√7/7

Used formulae:-

• Sin² A + Cos² A = 1

• Tan A = Sin A / Cos A