Question

If sin A = 3/4, Calculate cos A​

Answer 1

Step-by-step explanation:

Given:-

Sin A= 3/4

To find:-

Calculate cos A

Solution:-

Given Sin A=3/4

on squaring both sides then

=>(Sin A)^2 = (3/4)^2

=>Sin^2 A = 9/16

=>1- Sin^2 A = 1-(9/16)

=>Cos^2 A=(16-9)/16

=>Cos^2 A=7/16

=>Cos A=√(7/16)

Cos A=√7/4

(or)

Sin A= 3/4

=>Opposite side to angle A / Hypotenuse =3/4

Let the opposite side = 3x

Hypotenuse =4x

By Pythagoras theorem

Opposite side ^2+ Adjacent side^2 =Hypotenuse^2

=>(3x)^2+Adajacent side^2=(4x)^2

=>9x^2+adajacent side^2=16x²

=>Adajacent side^2=16x^2-9x^2

=>adjacent side^2=7x^2

=>Adjacent side=√(7x^2)

Adjacent side =√7 x

Now,

Cos A= Adjacent side / Hypotenuse

=>Cos A= √7 x/4x

Cos A=√7/4

Answer:-

The value of Cos A=√7/4

Used formulae:-

• Sin A= Opposite side to angle A / Hypotenuse
• Cos A=Adjacent side to angle A / Hypotenuse
• Sin^2 A+ Cos^2 A=1
• Sin^2A= 1-Cos^2 A