Exploring Even and Odd Trigonometric Identities

This video tutorial covers even and odd trigonometric identities. It begins with an introduction to even functions, explaining their symmetry across the y-axis, and provides examples using cosine and secant functions. The tutorial then shifts to odd functions, highlighting their rotational symmetry about the origin, with examples using sine and tangent functions. The video concludes with practical examples to illustrate these concepts, reinforcing the understanding of even and odd trigonometric identities.

What is a key characteristic of even functions?

• They are not symmetrical.

• They have rotational symmetry about the origin.

• They are symmetrical across the y-axis.

• They are symmetrical across the x-axis.

If a function is even, what happens to the function value when the sign of the x-coordinate is changed?

• The function value doubles.

• The function value remains the same.

• The function value changes sign.

• The function value is halved.

Which of the following trigonometric functions is even?

• Sine

• Cosine

• Tangent

• Cotangent

What is a key characteristic of odd functions?

• They are symmetrical across the x-axis.

• They are symmetrical across the y-axis.

• They have rotational symmetry about the origin.

• They are not symmetrical.

If a function is odd, what happens to the function value when the sign of the x-coordinate is changed?

• The function value changes sign.

• The function value is halved.

• The function value doubles.

• The function value remains the same.

Which of the following trigonometric functions is odd?

• None of the above

• Sine

• Secant

• Cosine

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

• -1.5

• 0.75

• 1.5

• -0.75

What is the value of cosine(-x) if cosine(x) = 0.2?

• 0.4

• -0.2

• -0.4

• 0.2

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

• -10.6

• 10.6

• -5.3

• 5.3

What is the value of secant(x) if secant(-x) = 2.9?

• -5.8

• 5.8

• -2.9

• 2.9