sin A = 1/2 corresponds to A = 30°.

The angle A for which sin A = 1/√2 is A = 45°.

Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (3/5)^2) = sqrt(1 - 9/25) = sqrt(16/25) = 4/5.

Using the identity tan A = sin A / cos A, we find cos A = 3/5, thus tan A = (4/5) / (3/5) = 4/3.

The double angle formula for sine is sin(2x) = 2sin(x)cos(x).

This is known as the Double Angle Identity for sine.

sin(x) = 0 at x = nπ, where n is any integer.

If sin(x) = 0, then cos(x) can be either 1 or -1 depending on the angle x.

tan(x) = sin(x)/cos(x). If sin(x) = 0, then tan(x) is undefined when cos(x) = 0.

sin(x) = 0 at x = nπ, where n is any integer, hence all of the above.

The angles where sin(x) = 1/2 are x = π/6 and x = 5π/6.

sin(x) = 1/2 at x = π/6 and x = 5π/6 in the interval [0, 2π].

sin(30°) = 1/2, so x = 30°.

The angles where sin(x) = 1/2 in the interval [0, 2π] are x = π/6 and x = 5π/6.

x = π/6 and 5π/6.

Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Thus, cos(x) = ±1/√2.

tan(x) = sin(x)/cos(x) = (1/√2)/(1/√2) = 1.

Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Therefore, cos(x) = 1/√2.

Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Therefore, cos(x) = ±4/5. The positive value is taken as x is in the first quadrant.

Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Therefore, cos(x) = ±4/5.

Using sin^2(α) + cos^2(α) = 1, we find cos(α) = √(1 - 0.6^2) = √(1 - 0.36) = √0.64 = 0.8.

The angles where sin(θ) = 0 in the interval [0, 2π] are θ = 0 and θ = π.

sin(θ) = 0 at θ = 0° and 180°.

Using the identity sin^2(θ) + cos^2(θ) = 1, we have cos^2(θ) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Thus, cos(θ) = ±1/√2.

sin(θ) = 1/√2 at θ = 45°.

sin(θ) = 1/√2 at θ = 45° and θ = 225°.

sin(θ) = 1/√2 at θ = 45°.

Using the Pythagorean identity, cos(θ) = √(1 - sin²(θ)) = √(1 - (3/5)²) = 4/5.

Using the identity tan(θ) = sin(θ)/cos(θ) and cos(θ) = √(1 - sin^2(θ)), we find cos(θ) = 3/5. Thus, tan(θ) = (4/5)/(3/5) = 4/3.

The equation sin^(-1)(x) + cos^(-1)(x) = π/2 holds for all x in the domain of the functions, which is [-1, 1]. Therefore, x can be any value in this range.