Trigonometry Mastery Challenge

Graph the function y = sin(x) for one full period.

• Graph the function y = sin(x) with key points at (0,0), (π,1), (2π,0), and (3π,-1).

• Graph the function y = sin(x) from x = -π to x = π.

• Graph the function y = cos(x) from x = 0 to x = 2π.

• Graph the function y = sin(x) from x = 0 to x = 2π, showing the wave pattern with key points at (0,0), (π/2,1), (π,0), (3π/2,-1), and (2π,0).

Using the unit circle, find the coordinates of the point at 3π/4 radians.

• (√2/2, -√2/2)

• (-1, 0)

• (0, 1)

• (-√2/2, √2/2)

Solve the equation 2cos(x) - 1 = 0 for x in the interval [0, 2π].

• π/2

• ["π/3", "5π/3"]

• 3π/4

• π/4

Graph the function y = tan(x) and identify its asymptotes.

• The asymptotes of y = tan(x) are at x = (π/2) + nπ, where n is any integer.

• The asymptotes of y = tan(x) are at x = nπ, where n is any integer.

• The asymptotes of y = tan(x) are at x = (π/4) + nπ, where n is any integer.

• The asymptotes of y = tan(x) are at x = (3π/2) + nπ, where n is any integer.

Using the unit circle, determine the value of sin(5π/6).

• -1/2

• 1

• 1/2

• √3/2