Graphing Trigonometric Functions Quiz! Exam

1) Select the equation represented by the graph below.

Y = .5cos(x)

Y = sec(x)

Y = csc(x)

Y = 2sin(x)

Y = -cos(x)

The graph represents a cosine function with a negative amplitude. The equation y = -cos(x) matches this graph because it is a cosine function with a negative coefficient, which reflects the graph across the x-axis.

Explanation

The graph represents a cosine function with a negative amplitude. The equation y = -cos(x) matches this graph because it is a cosine function with a negative coefficient, which reflects the graph across the x-axis.

2) Select the equation represented by the graph below.

Y = cos(x)

Y = sin(x)

Y = tan(x)

Y = -sin(x)

Y = 2cos(x)

The graph represents a cosine function because it follows the shape of a cosine wave. The graph starts at the maximum point, then decreases to the minimum point, and continues to repeat this pattern. This is characteristic of a cosine function.

Explanation

The graph represents a cosine function because it follows the shape of a cosine wave. The graph starts at the maximum point, then decreases to the minimum point, and continues to repeat this pattern. This is characteristic of a cosine function.

3) Select the equation represented by the graph below.

Y = cos(x)

Y = sin(x)

Y = tan(x)

Y = -sin(x)

Y = 2cos(x)

The graph represents a sine function because it follows the shape of a sine wave. The graph starts at the origin, reaches a maximum point at π/2, then decreases to a minimum point at π, and continues to repeat this pattern. Therefore, the equation that best matches the graph is y = sin(x).

Explanation

The graph represents a sine function because it follows the shape of a sine wave. The graph starts at the origin, reaches a maximum point at π/2, then decreases to a minimum point at π, and continues to repeat this pattern. Therefore, the equation that best matches the graph is y = sin(x).

4) Select the equation represented by the graph below.

Y = cos(x)

Y = sin(x)

Y = tan(x)

Y = -sin(x)

Y = 2cos(x)

The graph represents a wave-like pattern that starts at the origin and oscillates between positive and negative values. This is characteristic of the sine function. Among the given options, the equation y = -sin(x) is the only one that matches this pattern.

Explanation

The graph represents a wave-like pattern that starts at the origin and oscillates between positive and negative values. This is characteristic of the sine function. Among the given options, the equation y = -sin(x) is the only one that matches this pattern.

5) Any situation that can be modeled with a sine function can also be modeled with a cosine function.

True

False

The statement is true because the sine and cosine functions are closely related. They have the same shape and period, but they are shifted by a phase difference of 90 degrees. This means that any function that can be represented by a sine function can also be represented by a cosine function by adjusting the phase shift.

Explanation

The statement is true because the sine and cosine functions are closely related. They have the same shape and period, but they are shifted by a phase difference of 90 degrees. This means that any function that can be represented by a sine function can also be represented by a cosine function by adjusting the phase shift.

6) Select the equation represented by the graph below.

Y = .5cos(x)

Y = 2sin(x)

Y = 2cos(x)

Y = .5sin(x)

Y = sin(x)

The graph shown in the question represents a sine wave that has been stretched vertically by a factor of 2. The equation y = 2sin(x) is the only option that matches this graph, as it represents a sine wave with an amplitude of 2. The other equations either have different amplitudes or represent cosine waves instead of sine waves.

Explanation

The graph shown in the question represents a sine wave that has been stretched vertically by a factor of 2. The equation y = 2sin(x) is the only option that matches this graph, as it represents a sine wave with an amplitude of 2. The other equations either have different amplitudes or represent cosine waves instead of sine waves.

7) Select the equation represented by the graph below.

Y = .5cos(x)

Y = 2sin(x)

Y = 2cos(x)

Y = .5sin(x)

Y = sin(x)

The graph represents a cosine function with a maximum amplitude of 0.5. The other options, y = 2sin(x), y = 2cos(x), y = .5sin(x), and y = sin(x), have amplitudes greater than 0.5, which do not match the graph. Therefore, the correct equation is y = 0.5cos(x).

Explanation

The graph represents a cosine function with a maximum amplitude of 0.5. The other options, y = 2sin(x), y = 2cos(x), y = .5sin(x), and y = sin(x), have amplitudes greater than 0.5, which do not match the graph. Therefore, the correct equation is y = 0.5cos(x).

8) Select the equation represented by the graph below.

Y = sec(x)

Y = tan(x)

Y = -csc(x)

Y = cot(x)

Y = sin(x)

The graph shown represents the function y = -csc(x). This can be determined by observing the shape of the graph, which resembles the graph of the cosecant function. Additionally, the negative sign indicates that the graph is reflected across the x-axis, which is consistent with the graph shown.

Explanation

The graph shown represents the function y = -csc(x). This can be determined by observing the shape of the graph, which resembles the graph of the cosecant function. Additionally, the negative sign indicates that the graph is reflected across the x-axis, which is consistent with the graph shown.

9) Select the equation represented by the graph below.

Y = sec(x)

Y = tan(x)

Y = -csc(x)

Y = cot(x)

Y = sin(x)

The graph represents the secant function, which is the reciprocal of the cosine function. The graph has a repeating pattern of peaks and valleys, with asymptotes at the points where the cosine function equals zero. This matches the characteristics of the secant function, making it the correct answer.

Explanation

The graph represents the secant function, which is the reciprocal of the cosine function. The graph has a repeating pattern of peaks and valleys, with asymptotes at the points where the cosine function equals zero. This matches the characteristics of the secant function, making it the correct answer.

10) Select the equation represented by the graph below.

Y = -tan(x)

Y = sec(x)

Y = 2sin(x)

Y = -csc(x)

Y = cot(x)

The graph represents a periodic function that starts at positive infinity and approaches negative infinity as x approaches pi/2. This behavior is consistent with the graph of y = cot(x), which is the reciprocal of the tangent function. Therefore, the correct equation represented by the graph is y = cot(x).

Explanation

The graph represents a periodic function that starts at positive infinity and approaches negative infinity as x approaches pi/2. This behavior is consistent with the graph of y = cot(x), which is the reciprocal of the tangent function. Therefore, the correct equation represented by the graph is y = cot(x).