Trigonometric Challenge

Graph the function y = sin(x) for x in the interval [-2π, 2π].

• The graph of y = sin(x) for x in the interval [-2π, 2π] is a sine curve that starts at (−2π, 0), reaches its peak at (0, 1), crosses the x-axis at (π, 0), reaches its lowest point at (2π, −1), and returns to the x-axis at (3π, 0).

• The graph of y = sin(x) is a straight line

• The graph of y = sin(x) is a parabola

• The graph of y = sin(x) is a hyperbola

Solve for x in the equation sin(x) = 0.5.

• x = 2π/3 or x = 120 degrees

• x = π/3 or x = 60 degrees

• x = π/4 or x = 45 degrees

• x = π/6 or x = 30 degrees

Graph the function y = cos(x) for x in the interval [-π, π].

• Graph plotted with two complete cycles of cosine function from -π to π.

• Graph plotted with sine function instead of cosine function.

• Graph plotted with exponential function.

• Graph plotted with one complete cycle of cosine function from -π to π.

Find the exact value of sin^(-1)(1).

• π/2

• 2π

• π

• 0

Graph the function y = tan(x) for x in the interval [-π/2, π/2].

• Graphing the function y = tan(x) for x in the interval [-π/2, π/2] results in a curve with vertical asymptotes at x = -π/2 and x = π/2.

• The function y = tan(x) has no asymptotes in the given interval

• Graphing the function y = tan(x) for x in the interval [-π/2, π/2] results in a straight line

• The graph of y = tan(x) is a perfect circle

Determine the value of cos^(-1)(0).

• 3pi/2

• pi/2

• pi

• pi/4

Graph the function y = csc(x) for x in the interval [0, 2π].

• The graph of y = csc(x) has a horizontal asymptote at x = π

• The graph of y = csc(x) is symmetric about the y-axis

• The graph of y = csc(x) for x in the interval [0, 2π] will have vertical asymptotes at x = 0, x = π, and x = 2π. It will have peaks at x = π/2 and x = 3π/2. The graph will repeat every π units.

• The graph of y = csc(x) has a peak at x = 2π

Calculate the value of tan^(-1)(√3).

• π/3

• 2π/3

• π/4

• π/6

Graph the function y = sec(x) for x in the interval [0, 2π].

• The graph of y = sec(x) has no asymptotes.

• The graph of y = sec(x) has a peak at x = π/2.

• The graph of y = sec(x) has a valley at x = 3π/2.

• The graph of y = sec(x) for x in the interval [0, 2π] will have vertical asymptotes at x = π/2 and x = 3π/2, and peaks at x = 0 and x = 2π, with valleys at x = π.

Solve for x in the equation cos(x) = -0.5.

• x = 3π/4 or x = 7π/4

• x = 2π/5 or x = 3π/5

• x = π/3 or x = 2π/3

• x = 4π/3 or x = 5π/3