Understanding Sine and Cosine Functions

The video tutorial guides viewers through determining a trigonometric function from a graph. It explains how to identify whether the function is sine or cosine based on its behavior at x=0. The tutorial then calculates the amplitude and period of the function, ultimately determining the values of 'a' and 'b' in the function y = a cos(bx). The video concludes by confirming the function as y = -2 cos(3x).

What is the main goal of the problem discussed in the video?

• To determine the type of function and its parameters from a graph.

• To calculate the area under a curve.

• To solve a quadratic equation.

• To find the derivative of a function.

Why can't the function be a sine function if it equals -2 when x is 0?

• Because sine of 0 is always 1.

• Because cosine of 0 is always -1.

• Because cosine of 0 is always 0.

• Because sine of 0 is always 0.

What is the value of 'a' in the function y = a cos(bx) if the function equals -2 when x is 0?

• -1

• -2

• 2

• 1

What does the amplitude of a cosine function represent?

• The distance from the maximum to the minimum value.

• The distance from the center to the maximum value.

• The frequency of the wave.

• The total height of the wave.

How is the period of a cosine function related to the value of 'b'?

• Period is equal to b times 2π.

• Period is equal to b divided by 2π.

• Period is equal to 2π divided by b.

• Period is equal to 2π times b.

If the period of the function is 2π/3, what is the value of 'b'?

• 1

• 2

• 3

• 4

What is the final form of the function discussed in the video?

• y = 2 cos(3x)

• y = -2 sin(3x)

• y = 2 sin(3x)

• y = -2 cos(3x)

Why can 'b' be either positive or negative in the cosine function?

• Because cosine is an even function.

• Because cosine is an odd function.

• Because sine is an even function.

• Because sine is an odd function.

What happens to the x-coordinate on the unit circle when moving in the positive angle direction?

• It starts at 0 and increases.

• It starts at 1 and decreases.

• It starts at -1 and increases.

• It starts at 0 and decreases.

What is the significance of the unit circle in understanding cosine functions?

• It helps in understanding the amplitude.

• It helps in understanding the y-coordinate behavior.

• It helps in understanding the period.

• It helps in understanding the x-coordinate behavior.