Exploring Odd-Even Identities in Mathematics

The video tutorial by Mr. Banker explores odd and even identities in mathematics, focusing on their graphical representations and applications in trigonometric functions. It explains the symmetry properties of odd and even functions, using examples like cubic graphs and parabolas. The tutorial further delves into the odd and even nature of sine, cosine, and tangent functions, providing identities for each. An example problem is solved to demonstrate the application of these identities, reinforcing the concepts discussed.

What type of symmetry does an odd function have?

• No symmetry

• Origin symmetry

• X-axis symmetry

• Y-axis symmetry

Which of the following is a classic example of an even function?

• Linear graph

• Cubic graph

• Exponential graph

• Parabola

What is the symmetry of a sine function?

• No symmetry

• X-axis symmetry

• Y-axis symmetry

• Origin symmetry

Which trigonometric function is considered even?

• Sine

• Cosecant

• Cosine

• Tangent

What happens to the sine of a negative angle?

• It becomes the opposite of the sine of the positive angle

• It becomes positive

• It remains the same

• It becomes zero

If the tangent of an angle is odd, what can be said about its reciprocal?

• It is undefined

• It is even

• It is odd

• It is neither odd nor even

What is the value of the cosine of a negative angle?

• It is undefined

• It is zero

• It is the opposite of the cosine of the positive angle

• It is the same as the cosine of the positive angle

What is the reciprocal of an even trigonometric function?

• Odd

• Even

• Neither odd nor even

• Undefined

What is the sine of theta minus pi over 2 equivalent to?

• Sine of theta

• Negative sine of theta

• Negative cosine of theta

• Cosine of theta

If the cosine of theta is 0.34, what is the sine of theta minus pi over 2?

• 0.34

• -0.34

• -0.68

• 0.68