Question

if sin theta = x/y find the value of cos theta and ban theta
in terms of x and y​

Answer 1

Step-by-step explanation:

GIVEN:- sinθ = x/y

it can be done by 2/3 ways

we know, sinθ = perpendicular/hypotenuse = x/y

so by Pythagoras theorem,

base² = hypotenuse² - perpendicular ²

=> base² = y² - x²

=> base = √(y²-x²)

so, cosθ = base/hypotenuse

=> cosθ = √(y²-x²)/y

and. tanθ = perpendicular/base

=> tanθ = x/√(y²-x²)

another method,

we know : cosθ = √(1-sin²θ)

=> cosθ = √(1 - x²/y²)

=> cosθ = √{(y²-x²)/y²}

=> cosθ = √(y²-x²)/y

and tanθ = sinθ/cosθ

=> tanθ = x/y / √(y²-x²)/y

=> tanθ = x/√(y²-x²)

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