Exploring Even and Odd Identities in Trigonometry

The video tutorial explains the even and odd identities in trigonometry, focusing on how they help handle negative angles. It discusses the symmetry of sine and cosine functions, identifying sine as an odd function and cosine as an even function. The tutorial provides examples to demonstrate how these identities simplify calculations involving negative angles, emphasizing the importance of understanding the symmetry in trigonometric functions.

What is the primary benefit of using even and odd identities in trigonometry?

• They are essential for integration.

• They are used to find the derivatives of trigonometric functions.

• They help in solving algebraic equations.

• They simplify the calculation of trigonometric functions for negative angles.

Which trigonometric function is classified as an odd function?

• Cosine

• Sine

• Secant

• Cosecant

Why is cosine considered an even function?

• It is symmetric with respect to the line y=x.

• It is symmetric around the x-axis.

• It is symmetric around the y-axis.

• It is symmetric with respect to the origin.

What value do you get when you plug in negative pi over 2 into the sine function?

• Undefined

• 0

• 1

• -1

What happens to the value of cosine when you plug in a negative angle?

• It becomes undefined.

• It remains the same.

• It becomes negative.

• It becomes zero.

Which trigonometric function behaves exactly like cosine when dealing with negative angles?

• Sine

• Tangent

• Secant

• Cosecant

How is the tangent function affected by negative angles?

• The negative sign is moved out front.

• The value becomes zero.

• The negative sign is ignored.

• The value becomes undefined.

What is the value of sine of negative 30 degrees?

• -1/2

• 0

• 1/2

• -1

What is the value of cosine of negative 45 degrees?

• -Square root of 2 over 2

• 1

• Square root of 2 over 2

• -1

What is the value of tangent of negative 45 degrees?

• 1

• 0

• -1

• Undefined