Trigonometric Graphs: Sin, Cos, and Tan Practice

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Designed for 11th grade math students. State the coordinates, key features, or sketch details for each item without using a graphing calculator.

What are the coordinates of the maximum value of y = sin(x) in the interval [0, 2π]?
What is the y-intercept of y = cos(x)?
State the period of the function y = tan(x) in radians.
List all zeros (x-intercepts) of y = sin(x) on the interval [0, 2π].
Give the equations of two vertical asymptotes for y = tan(x) closest to the y-axis.
State the domain and range of y = cos(x).
What are the coordinates of the minimum value of y = cos(x) on [0, 2π]?
What is the value of tan(x) at x = π/4 and x = -π/4?

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Trigonometric Graphs: Sin, Cos, and Tan Practice

Answer key

What are the coordinates of the maximum value of y = sin(x) in the interval [0, 2π]?
(π/2, 1)
What is the y-intercept of y = cos(x)?
(0, 1)
State the period of the function y = tan(x) in radians.
π radians
List all zeros (x-intercepts) of y = sin(x) on the interval [0, 2π].
x = 0, x = π, and x = 2π
Give the equations of two vertical asymptotes for y = tan(x) closest to the y-axis.
x = -π/2 and x = π/2
State the domain and range of y = cos(x).
Domain: all real numbers (-∞, ∞); Range: [-1, 1]
What are the coordinates of the minimum value of y = cos(x) on [0, 2π]?
(π, -1)
What is the value of tan(x) at x = π/4 and x = -π/4?
tan(π/4) = 1; tan(-π/4) = -1