Exercises
Explore how trigonometric graphs change under common transformations in this quiz on sine, cosine, and tangent functions. Test your understanding of amplitude, period, frequency, reflections across the x-axis, and horizontal and vertical shifts. Questions examine functions such as 3sin(x), cos(2x), tan(x) + 4, sin(4x), sin(x - π/2), and -2sin(x) + 5. You will identify how coefficients and constants affect a graph’s height, cycle length, position, and direction. This quiz is ideal for students building confidence with graphing and interpreting transformed trigonometric functions.
Answer the questions below and check the explanation for each answer.
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The amplitude of a sine function a*sin(x) is given by the absolute value of a. In this case, it's 3.
A negative sign before a function like y = -sin(x) reflects the graph over the x-axis.
The period of cos(kx) is 2π/k. For cos(2x), the period is π.
A function of the form f(x) = tan(x) + c implies a vertical shift. Here, it's shifted 4 units upwards.
Frequency is the reciprocal of the period. Given f(x) = sin(4x), the period is π/2, making the frequency 4.
The function sin(x - c) results in a horizontal shift right if c is negative. Here, right by π/2 units.
The term +5 indicates a vertical shift upward by 5 units.
The constant +1 indicates a vertical shift upward by 1 unit.
The period of sin(kx) is 2π/k. For sin(x/3), the period is 6π.
The coefficient before sin(x) gives an amplitude of 2, and +3 indicates an upward shift of 3.
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