Sine and Cosine Function Graphs

Front

What is the range of the function y = -3cos(x) - 2?

Back

The range is [-5, -1]. The maximum value is -2 (when cos(x) = -1) and the minimum value is -5 (when cos(x) = 1).

Front

What is the amplitude of the wave represented by the function y = -3cos(x)?

Back

The amplitude is 3. Amplitude is the absolute value of the coefficient of the cosine function.

Front

What is the general form of a sine function?

Back

The general form is y = A sin(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

How do you determine the period of a sine function?

Back

The period of a sine function y = A sin(Bx) is given by the formula: Period = \frac{2\pi}{|B|}.

Front

What is the amplitude of the wave represented by the function y = 4sin(x)?

Back

The amplitude is 4. It is the coefficient of the sine function.

Front

What is the period of the function y = sin(3x)?

Back

The period is \frac{2\pi}{3}. This is calculated using the formula for the period.

Front

What does a negative coefficient in front of a cosine function indicate?

Back

A negative coefficient indicates a reflection over the x-axis.

Front

What is the equation of a sine wave with an amplitude of 10 and a period of \frac{5\pi}{4}?

Back

The equation is f(t) = 10sin(\frac{8}{5}t). The amplitude is 10 and the period is calculated to find the coefficient of t.

Front

What is the value of x at point P for the function y = cos(5x)?

Back

The value of x at point P is \frac{2\pi}{5}. This is determined by analyzing the graph.

Front

How do you find the maximum and minimum values of a cosine function?

Back

The maximum value is the vertical shift plus the amplitude, and the minimum value is the vertical shift minus the amplitude.