Trigonometric Functions and Transformations

The video tutorial explores the relationship between sine and cosine, particularly focusing on the identity sine of 90 degrees minus x equals cosine of x. The instructor provides two explanations: a simple one using right angle triangles and a more advanced one using the unit circle. The video also covers the graphical representation of these functions, discussing symmetry and the effects of horizontal and vertical flips. The tutorial concludes with practical applications of these concepts, emphasizing the importance of understanding trigonometric identities and graph shifts.

What is the result of sine of 90 degrees minus x?

• cot x

• sin x

• cos x

• tan x

In the context of right angle triangles, what is sine of 90 degrees minus x equivalent to?

• Adjacent over hypotenuse

• Opposite over adjacent

• Opposite over hypotenuse

• Adjacent over opposite

Why is the first explanation using right angle triangles insufficient?

• It doesn't use the unit circle

• It doesn't account for negative angles

• It only applies to obtuse angles

• It only applies to acute angles

What is the significance of the unit circle in trigonometry?

• It is irrelevant to trigonometric functions

• It helps in understanding acute angles

• It is only used for angles greater than 90 degrees

• It is used to define sine and cosine for all angles

What does a negative sign in front of x in a trigonometric function indicate?

• A vertical flip

• A horizontal flip

• No change

• A shift to the right

What type of function is sine, based on its symmetry properties?

• Odd function

• Even function

• Neither even nor odd

• Both even and odd

How does a negative sign affect the graph of a trigonometric function when applied to y?

• It shifts the graph to the right

• It shifts the graph to the left

• It flips the graph vertically

• It flips the graph horizontally

What happens to the graph of cos(x) when it is transformed to cos(-x)?

• It flips vertically

• It shifts upwards

• It remains unchanged

• It flips horizontally

What is the effect of x minus a constant on the graph of a trigonometric function?

• It shifts the graph to the left

• It flips the graph vertically

• It shifts the graph to the right

• It flips the graph horizontally

Why is it important to understand the effect of negative signs on x and y in trigonometric functions?

• To calculate the graph's frequency

• To predict the graph's color

• To determine the graph's amplitude

• To understand graph transformations