Sine Function Properties and Effects

The video tutorial explores transformations of trigonometric functions, focusing on sine and cosine. It begins with a review of basic function transformations, using y = 2sin(θ) as an example to illustrate changes in amplitude. The tutorial then shifts to radians and key angles, emphasizing the importance of understanding these concepts in trigonometry. The video further examines the transformation y = sin(2θ), explaining how altering the angle affects the function's frequency. Throughout, the unit circle is used as a tool to visualize and understand these transformations.

What happens to the graph of y = x² when it is multiplied by 2?

• It shifts to the left.

• It becomes wider.

• It shifts to the right.

• It becomes narrower.

How does multiplying the sine function by 2 affect its graph?

• The amplitude doubles.

• The graph becomes narrower.

• The amplitude halves.

• The graph becomes wider.

What is the new maximum value of y = 2 sin(θ) compared to y = sin(θ)?

• 1

• 2

• -1

• 0

In the context of the sine function, what is the significance of the angle 3π/2?

• It is the maximum point.

• It is the minimum point.

• It is a zero crossing point.

• It is the starting point.

What is the value of a full revolution in radians?

• 4π

• 3π

• 2π

• π

How does the graph of y = sin(2θ) differ from y = sin(θ)?

• It is compressed horizontally.

• It is shifted upwards.

• It is stretched vertically.

• It is shifted downwards.

What happens to the period of the sine function when the angle is multiplied by 2?

• The period becomes zero.

• The period remains the same.

• The period halves.

• The period doubles.

If y = sin(2θ), what is the value of y when θ = π?

• 2

• 0

• 1

• -1

What is the effect of placing a constant inside the sine function's angle?

• It affects the vertical shift.

• It affects the phase shift.

• It affects the period.

• It affects the amplitude.

What is the sine of 3π in the unit circle?

• 1

• 0

• 2

• -1