Trigonometric Identities and Functions

The video tutorial explains how to simplify the tangent of (PI/2 - X) using sum or difference angle identities. Initially, the tangent identity is attempted, but it fails due to the undefined nature of tangent PI/2. The tutorial then demonstrates rewriting tangent as sine over cosine, allowing the use of sine and cosine identities to simplify the expression to cotangent X. The video concludes by mentioning the cofunction identity as an easier alternative, though not used due to the given instructions.

What is the initial goal when simplifying the tangent of the expression pi/2 - x?

• To convert it into a sine function

• To find its exact numerical value

• To simplify it to a single trigonometric function

• To express it as a product of two functions

Why can't the tangent identity be used for pi/2 - x?

• Because tangent pi/2 is zero

• Because tangent pi/2 is undefined

• Because tangent pi/2 is negative

• Because tangent pi/2 is a complex number

What is the alternative approach to simplify the tangent expression?

• Rewriting tangent as sine divided by cosine

• Using the Pythagorean identity

• Using the double angle formula

• Applying the half-angle identity

What is the value of sine(pi/2)?

• 1

• Undefined

• 0

• -1

What is the value of cosine(pi/2)?

• 0

• Undefined

• 1

• -1

What does the expression simplify to after using sine and cosine identities?

• Cotangent x

• Secant x

• Cosecant x

• Tangent x

What is the result of dividing cosine x by sine x?

• Tangent x

• Cotangent x

• Secant x

• Cosecant x

What identity could have been used to simplify the expression more easily?

• Half-angle identity

• Double angle identity

• Cofunction identity

• Pythagorean identity

What is the relationship between tangent and cotangent in terms of cofunction identities?

• Tangent of an angle is equal to cosine of its complement

• Tangent of an angle is equal to cotangent of its complement

• Tangent of an angle is equal to cotangent of the same angle

• Tangent of an angle is equal to sine of its complement

What was the main instruction given for solving the problem?

• Use a cofunction identity

• Use a double angle identity

• Use a sum or difference angle identity

• Use a half-angle identity