Find the sinθ and cosθ, if cotθ=4 and 0<θ<pi/2.

Answer 1

Draw a right triangle with an acute angle θ.

cotθ = adjacent/opposite = 4/1

So, if the side opposite θ has length 1 then the side adjacent to θ has length 4. By the Pythagorean Theorem, the hypotenuse would then have length √17.

cosθ = adjacent / hypotenuse = 4/√17 = 4√17 / 17 and sinθ = opposite / hypotenuse = 1/√17 = √17/17.

Answer 2

Use relations

sinθ=+/-(1/√(1+cot²θ))

and

cosθ=(+/-)(cotθ/√(1+cot²θ))