Understanding Trigonometric Functions: Odd and Even

The video tutorial explains how to determine trigonometric function values based on whether the function is odd or even. It covers the properties of even functions like cosine and secant, which are symmetrical across the y-axis, and odd functions like sine, cosecant, tangent, and cotangent, which have rotational symmetry about the origin. The tutorial provides examples and graphical representations to illustrate these concepts, showing how changing the sign of the input affects the function values.

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.