Even and Odd Functions in Trigonometry

The video tutorial covers even and odd trigonometric identities, explaining their properties and symmetry. Even functions are symmetrical across the y-axis, while odd functions have rotational symmetry about the origin. The video provides examples of these identities using trigonometric functions like sine, cosine, tangent, and secant, illustrating how their values change with sign changes in the input.

What is the main goal of the video on even and odd trigonometric identities?

• To explore the history of trigonometry

• To learn about calculus applications

• To state and illustrate even and odd trig identities

• To solve complex trigonometric equations

Which of the following is true about even functions?

• They are symmetrical about the origin

• They are symmetrical across the Y-axis

• They have no symmetry

• They are symmetrical across the X-axis

If f(x) is an even function, what is the relationship between f(x) and f(-x)?

• f(x) = -f(-x)

• f(x) = f(-x)

• f(x) = 2f(-x)

• f(x) = 0

What type of symmetry do odd functions exhibit?

• No symmetry

• Symmetry across the Y-axis

• Symmetry across the X-axis

• Rotational symmetry about the origin

Which trigonometric function is an example of an odd function?

• Cosine

• Secant

• Sine

• Cosecant

If f(x) is an odd function, what is the relationship between f(x) and f(-x)?

• f(x) = -f(-x)

• f(x) = 0

• f(x) = f(-x)

• f(x) = 2f(-x)

What is the value of sine(-x) if sine(x) = 0.75?

• 0

• 1.5

• 0.75

• -0.75

If cosine(x) = 0.2, what is cosine(-x)?

• -0.2

• 0

• 0.2

• 1.0

What is the value of tangent(-x) if tangent(x) = 5.3?

• -5.3

• 10.6

• 5.3

• 0

If secant(-x) = 2.9, what is secant(x)?

• 5.8

• 0

• 2.9

• -2.9