Understanding Trigonometric Identities

The video tutorial explains how to use sum and difference identities to simplify the expression tangent of pi over two minus u. It highlights that tangent at pi over two is undefined and explores this through graphing and unit circle analysis. The tutorial attempts to apply the difference identity for tangent but finds it ineffective due to the undefined nature of tangent at pi over two. Instead, it uses sine and cosine identities to simplify the expression, ultimately showing that tangent of pi over two minus u simplifies to cotangent u, provided u is not a multiple of pi. The video concludes with a brief explanation of the homework task.

What is another name for addition or subtraction formulas in trigonometry?

• Reciprocal identities

• Sum or difference identities

• Product identities

• Quotient identities

Why is the tangent of pi over two considered undefined?

• Because it equals zero

• Because it results in division by zero

• Because it is a negative value

• Because it equals one

What is the period of the tangent function?

• 4 pi radians

• Pi/2 radians

• Pi radians

• 2 pi radians

What happens when you apply the difference identity for tangent at pi over two?

• It simplifies to one

• It simplifies to zero

• It results in a valid expression

• It cannot be evaluated due to undefined values

Which identity is used to express tangent in terms of sine and cosine?

• Product identity

• Reciprocal identity

• Quotient identity

• Pythagorean identity

What is the value of sine at pi over two?

• Undefined

• Negative one

• One

• Zero

What is the value of cosine at pi over two?

• Zero

• One

• Negative one

• Undefined

What is the result of simplifying tangent of pi over two minus u using sine and cosine identities?

• Secant u

• Cosine u

• Cotangent u

• Sine u

In the context of the video, what does f(u) equal?

• Sine u

• Cosine u

• Cotangent u

• u

What is the condition for the expression tangent of pi over two minus u to be defined?

• u is a multiple of pi

• u is a multiple of pi/2

• u is not a multiple of pi/2

• u is not a multiple of pi