Trigonometry Challenge

Graph the function y = sin(x) for 0 ≤ x ≤ 2π.

• The graph of y = sin(x) for 0 ≤ x ≤ 2π is a wave that starts at (0, 0), reaches its peak at (π/2, 1), goes back to 0 at (π, 0), reaches its minimum at (3π/2, -1), and returns to 0 at (2π, 0).

• The graph of y = sin(x) for 0 ≤ x ≤ 2π is a straight line

• The graph of y = sin(x) for 0 ≤ x ≤ 2π is a parabola

• The graph of y = sin(x) for 0 ≤ x ≤ 2π is a circle

What are the coordinates of the point on the unit circle corresponding to an angle of 60 degrees?

• (1, 0)

• (0, 1)

• (√3/2, 0)

• (0.5, √3/2)

In a right triangle, if the opposite side is 5 and the hypotenuse is 13, what is the sine of the angle opposite the side of length 5?

• 3/5

• 7/13

• 5/12

• 5/13

Graph the function y = cos(x) for -π/2 ≤ x ≤ π/2.

• The graph of y = cos(x) for -π/2 ≤ x ≤ π/2 is a straight line

• The graph of y = cos(x) for -π/2 ≤ x ≤ π/2 is a parabola

• The graph of y = cos(x) for -π/2 ≤ x ≤ π/2 is a circle

• The graph of y = cos(x) for -π/2 ≤ x ≤ π/2 is a curve that starts at (−π/2, 0), reaches its peak at (0, 1), and ends at (π/2, 0).

What is the cosine of 0 degrees?

• 1

• 0

• 0.5

• -1

Solve the right triangle with an angle of 30 degrees and a hypotenuse of 10 units.

• Opposite side (height) = 6 units, Adjacent side (base) = 7.5 units

• Opposite side (height) = 4 units, Adjacent side (base) = 8.5 units

• Opposite side (height) = 3 units, Adjacent side (base) = 9.5 units

• Opposite side (height) = 5 units, Adjacent side (base) = 8.66 units

Graph the function y = tan(x) for -π/2 ≤ x ≤ π/2.

• Graph the function y = sin(x) for -π/2 ≤ x ≤ π/2

• Graph the function y = cot(x) for -π/2 ≤ x ≤ π/2

• Graph the function y = cos(x) for -π/2 ≤ x ≤ π/2

• Graph the function y = tan(x) for -π/2 ≤ x ≤ π/2 to show one period of the tangent function.

What is the tangent of 45 degrees?

• 0.5

• 3.14

• 2

• 1

In a right triangle, if the adjacent side is 4 and the hypotenuse is 5, what is the sine of the angle opposite the side of length 4?

• 0.4

• 0.8

• 0.6

• 1.2

Graph the function y = csc(x) for 0 ≤ x ≤ 2π.

• The graph of y = csc(x) for 0 ≤ x ≤ 2π will have vertical asymptotes at x = 0, π, and 2π, with peaks at these points and valleys at x = π/2 and 3π/2.

• The graph of y = csc(x) for 0 ≤ x ≤ 2π will have no asymptotes.

• The graph of y = csc(x) for 0 ≤ x ≤ 2π will have horizontal asymptotes at x = 0, π, and 2π.

• The graph of y = csc(x) for 0 ≤ x ≤ 2π will have peaks at x = π/4 and 3π/4.