Using tan(30) = height / 20, height = 20 * tan(30) = 20 * (1/√3) = 20/√3 = 10√3 meters.

Using tan(30°) = height/40, height = 40 * (1/√3) = 40/√3 = 20√3 meters.

sin(θ) = opposite/hypotenuse = 3/5

sin(x) = √3/2 gives x = 60° and 120°, so 2sin(x) = √3 gives x = 150°.

cos(x) = 0.5 gives x = 60° and 300°.

The amplitude is the coefficient in front of the cosine function, which is 3.

The frequency of y = sin(Bx) is |B|/(2π). Here, B = 2, so the frequency is 2/(2π) = 1/π.

Using tan(60°) = height/50, height = 50 * tan(60°) = 50√3.

The inverse of sin(x) is sin⁻¹(x).

The maximum value of a cosine function y = Acos(Bx) is |A|. Here, A = 2, so the maximum value is 2.

The maximum value occurs when cos(x) = -1, giving a maximum of -2 * -1 = 2.

The period of the sine function is 2π.

The period of the sine function is 2π, meaning it repeats every 2π units.

The phase shift is found by setting 2x + π = 0, leading to a shift of -π/2.

The range of y = 2sin(x) is [-2, 2] because the sine function oscillates between -1 and 1.

The range of y = Asin(Bx) is [-|A|, |A|]. Here, A = 4, so the range is [-4, 4].

cos(45°) = √2/2.

sec(θ) = 1/cos(θ) = 1/0.5 = 2.

The value of sin(π/6) is 1/2.

The vertical asymptotes of the tangent function occur at x = π/2 + nπ, where n is an integer.

The vertical shift of the function y = Asin(Bx) + D is D. Here, D = 2, so the vertical shift is 2 units up.

The vertical shift is determined by the constant added to the function, which is +2.

The x-intercept occurs when y = 0, which happens at x = 0 for cos(x) - 1.

The cosine function equals zero at x = π/2 and x = 3π/2. The x-intercepts in [0, 2π] are π/2 and 3π/2.

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

The Pythagorean identity is sin²x + cos²x = 1.

The amplitude of a sine function y = Asin(Bx) is |A|. Here, A = 3, so the amplitude is 3.

cot(x) = 1/tan(x) = cos(x)/sin(x).

cot(x) = cos(x)/sin(x) is the correct identity.

sin²(θ) + cos²(θ) = 1