Question

if sin theta=x/y then cos theta is​

Answer 1

Answer:

Step-by-step explanation:

Sin Q = x/y, Cos Q =?

We know that,

(Sin Q)^2 + (Cos Q)^2 = 1

or, Cos Q = +- √( 1 - (Sin Q)^2 )

= +- √( 1 - (x/y)^2 )

= +- √( (y^2 - x^2)/y^2 )

= +- √(y^2 - x^2)/y

Answer 2

Answer:

cos θ = √( y² - x² )/ y

Step-by-step explanation:

Given :-  sin θ = x/y

To Find :- Value of cos θ.

Solution :-

It is given that sin θ = x/y .

Its is known from trigonometric formulas that,

                            sin² θ+cos² θ = 1

From the above formula we can contemplate that,

                            cos² θ = 1-sin² θ

Putting the values now,

cos² θ = 1 - ( x/y )²

⇒ cos² θ = (y² - x² )/y²

Square root both the sides,

⇒ √cos² θ = √(y² - x² )/√y²

⇒ cos θ = √( y² - x² )/ y

Therefore, cos θ = √( y² - x² )/ y .

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