Use the Pythagorean identity sin^2 * 0 + cos^2 * 0 =1 to find cosθ. The angle θ is an acute angle.

Question

sin0 = square root of 2/4

Answer 1

To find cosθ using the Pythagorean identity, we substitute the given value of sinθ into the equation.

sinθ = √(2/4)

Next, we square both sides of the equation to eliminate the square root.

(sinθ)^2 = (√(2/4))^2

(sinθ)^2 = (2/4)

(sinθ)^2 = 1/2

Using the Pythagorean identity sin^2θ + cos^2θ = 1, we can now substitute the value of (sinθ)^2 into the equation.

(1/2) + cos^2θ = 1

cos^2θ = 1 - 1/2

cos^2θ = 1/2

To find the value of cosθ, we take the square root of both sides of the equation. Since θ is an acute angle, cosθ will be positive.

cosθ = √(1/2) = (√1)/(√2) = 1/√2

Simplifying the expression, we rationalize the denominator.

cosθ = (1/√2) * (√2/√2) = (√2)/2

Therefore, cosθ = (√2)/2.