Exercises
Mastering Trigonometric Graphs helps you check your understanding of sine, cosine, and tangent graph behavior. Explore essential concepts including period, amplitude, vertical and phase shifts, reflections, fundamental frequency, maximum values, and undefined points. Questions cover familiar functions such as y = sin(x), y = cos(x), and y = tan(x), along with transformed equations like y = 2sin(4x) and y = cos(x - Pi/2). Use this quiz to strengthen your ability to read, interpret, and transform trigonometric graphs for math class, revision, or exam preparation.
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The period of the sine function y = sin(x) is 2Pi. This means the sine wave repeats every 2Pi units along the x-axis.
Cosine function Cos(x) is equal to 1 at both 0 and 360 degrees. This is because cosine represents the x-coordinate on the unit circle where the angle intercepts.
The phase shift is determined by the horizontal transformation of cos(x). For y = cos(x - Pi/2), the graph shifts right by Pi/2.
The amplitude is the vertical stretch of the wave. For y = 3sin(x), the amplitude is 3, meaning it peaks at 3 and troughs at -3.
The whole function y = tan(x) is shifted 4 units up due to the addition of 4 to the function.
For y = tan(x), the function is undefined at x = Pi/2 because tangent, defined as the ratio sin(x)/cos(x), would involve division by zero.
The term inside the bracket, 4x, indicates the frequency is 4. The graph of sin(x) will complete 4 cycles every 2Pi units.
By multiplying the sine function y = sin(x) by -1, a vertical flip occurs over the x-axis.
y = cos(x) achieves its maximum value at x = 0 with cosine at 1, as the wave starts at its peak.
The horizontal shift of y = cos(x) by Pi to the left results in the equation y = cos(x + Pi), effectively flipping the phase.
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