Trigonometry Graphing Trig Functions 2

Question 1

What is the phase shift of y = sin(x − π/3)?

Accepted Answer

π/3 to the right

Answer

The phase shift is x − π/3 = 0 → x = π/3, shifting the graph π/3 units to the right.

Question 2

Which transformation does y = cos(x) + 3 represent?

Accepted Answer

Vertical shift up 3

Answer

Adding 3 outside the cosine function shifts the entire graph up 3 units (vertical translation).

Question 3

What is the period of y = tan(2x)?

Accepted Answer

π/2

Answer

The period of tangent is π/|b|, so π/2 = π/2.

Question 4

What is the vertical asymptote nearest to x = 0 for y = tan(x)?

Accepted Answer

x = π/2

Answer

Tangent is undefined when cos(x) = 0, which first occurs at x = π/2.

Question 5

The graph of y = −sin(x) is a reflection of y = sin(x) over which axis?

Accepted Answer

x-axis

Answer

Multiplying by −1 outside the function reflects the graph across the x-axis.

Trigonometry Practice Test