Using the identity sin^2(θ) + cos^2(θ) = 1, we have sin^2(θ) = 1 - (1/2)^2 = 1 - 1/4 = 3/4. Thus, sin(θ) = ±√3/2.

cos(30°) = 1/2, hence θ = 30°.

Using the identity cot θ = cos θ / sin θ, we find sin θ = 4/5.

Using the identity cot θ = cos θ / sin θ, we can find sin θ = 12/13 using the Pythagorean theorem: sin θ = 12/√(5^2 + 12^2) = 12/13.

Using the identity cot(x) = cos(x)/sin(x), we can find sin(x) = 12/13 using the Pythagorean theorem.

Since sec A = 1/cos A, we have cos A = 1/2.

Since sec θ = 1/cos θ, if sec θ = 2, then cos θ = 1/2.

sec(x) = 1/cos(x), so cos(x) = 1/2.

Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.

Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.

Using the identity tan A = sin A / cos A, we find cos A = sqrt(1 - (0.6)^2) = 0.8, thus tan A = 0.6 / 0.8 = 0.75.

sin A = 1/2 at A = 30° and A = 150°.

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.

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.

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.