Trigonometric Functions and Their Properties

The video tutorial covers the concepts of domain and range in functions and their inverses, emphasizing how they swap roles. It explains concavity and how it changes upon reflection, using sine and cosine functions as examples. The cosine function is analyzed with a focus on domain, range, and stationary points. The tangent function and its inverse are explored, highlighting the gradient at the origin and the importance of maintaining correct angles in graphing.

What happens to the domain and range when you find the inverse of a function?

• They both become zero.

• They swap around.

• They both become infinite.

• They remain the same.

What is the range of the sine function as discussed in the video?

• 0 to 2π

• -π/2 to π/2

• 0 to π

• -1 to 1

How does the concavity of sine x change when reflected across the y-axis?

• It remains concave down.

• It becomes concave up.

• It becomes linear.

• It becomes a constant function.

What type of symmetry does the sine function have?

• No symmetry

• Even symmetry

• Rotational symmetry

• Odd symmetry

What is the range of the cosine function as discussed in the video?

• 0 to π

• 0 to 2π

• -1 to 1

• -π/2 to π/2

Why are the endpoints of the cosine function important?

• They are the maximum and minimum values.

• They are points of inflection.

• They are where the function is undefined.

• They are turning points or stationary points.

What is the concavity of tan x in the first quadrant?

• Constant

• Linear

• Concave up

• Concave down

What is the gradient of tan x at the origin?

• Undefined

• 1

• -1

• 0

What is the domain restriction for the inverse tangent function?

• -π to π

• -π/2 to π/2

• 0 to π

• 0 to 2π

What should the gradient of the inverse tangent function be at the origin?

• Undefined

• -1

• 1

• 0