Understanding Trigonometric Functions: Odd and Even

What characteristic do even functions like cosine and secant share?

• They have rotational symmetry about the origin.

• They are symmetrical across the Y-axis.

• They are not symmetrical.

• They are symmetrical across the X-axis.

Which of the following is an odd function?

• None of the above

• Cosine

• Secant

• Sine

If sine(x) = 0.15, what is sine(-x)?

• 1

• 0.15

• -0.15

• 0

What is the value of tangent(x) if tangent(-x) = -3?

• -3

• 0

• 3

• 1

If secant(-x) = 1.4, what is secant(x)?

• -1.4

• 2.8

• 1.4

• 0

What does the graphical representation of even functions show?

• Symmetry about the origin

• No symmetry

• Symmetry across the X-axis

• Symmetry across the Y-axis

In the graphical representation, what is the value of f(-π/2) for cosine?

• 1

• 0

• -1

• π

What is the symmetry characteristic of odd functions like sine and tangent?

• No symmetry

• Rotational symmetry about the origin

• Symmetry across the Y-axis

• Symmetry across the X-axis

For the sine function, if f(π/2) = 1, what is f(-π/2)?

• 0

• π

• -1

• 1

What happens to the graph of an odd function when rotated 180 degrees about the origin?

• It becomes symmetrical across the Y-axis.

• It looks exactly the same.

• It becomes symmetrical across the X-axis.

• It looks different.