The tangent function has vertical asymptotes at x = π/2 + nπ, where n is an integer. The first asymptote in [0, π] is at π/2.

The period is calculated as 2π divided by the coefficient of x, which is 3, giving a period of 2π/3.

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.

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].

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

The phase shift is found by setting the inside of the sine function to zero, giving a shift of π/4 to the right.

The phase shift of y = sin(x - C) is C. Here, C = π/4, so the phase shift is π/4 to the right.