Sine and Cosine Function Concepts

The video tutorial explores graphing trigonometric functions using a graphing application from gcalc.net. It covers the sine, cosine, and tangent functions, discussing their properties such as period, amplitude, and how they oscillate. The tutorial also explains how changing coefficients affects the period and amplitude of these functions. The instructor uses the unit circle to explain the behavior of these functions and encourages viewers to think about the mathematical concepts involved.

What is the value of the sine function at 0 radians?

• 1

• 0

• -1

• Undefined

What is the amplitude of the sine function?

• 0

• 1

• -1

• 2

How does the cosine function differ from the sine function at 0 radians?

• Cosine is 0

• Cosine is 1

• Cosine is -1

• Cosine is undefined

How does the cosine function behave at π/2 radians?

• Cosine is 0

• Cosine is 1

• Cosine is undefined

• Cosine is -1

What is the period of the tangent function?

• π/2

• 4π

• π

• 2π

What is the relationship between sine and tangent functions?

• Tangent is sine plus cosine

• Tangent is sine over cosine

• Tangent is sine times cosine

• Tangent is cosine over sine

What happens to the period of the sine function when the coefficient of x is increased?

• Period remains the same

• Period becomes undefined

• Period decreases

• Period increases

What effect does a coefficient less than 1 have on the sine function's period?

• Period increases

• Period decreases

• Period remains the same

• Period becomes undefined

If the sine function is multiplied by 2, what happens to its amplitude?

• Amplitude becomes 0.5

• Amplitude becomes 2

• Amplitude remains 1

• Amplitude becomes -2

What happens to the amplitude when the sine function is multiplied by 0.5?

• Amplitude remains 1

• Amplitude becomes 2

• Amplitude becomes -0.5

• Amplitude becomes 0.5