Understanding Limits with Trigonometric Functions

This video tutorial explores the concept of limits involving trigonometric functions, focusing on sine, cosine, tangent, and cotangent. It explains how to find limits as x approaches specific values, emphasizing the continuity of sine and cosine over all real numbers. The video also discusses the domain constraints of tangent and cotangent, highlighting situations where limits do not exist due to undefined values.

What is the limit of sine of x as x approaches pi?

• 1

• Undefined

• 0

• -1

Why are sine and cosine continuous over all real numbers?

• They are only defined for positive numbers

• They are periodic functions

• They have a finite range

• They are defined and continuous over their entire domain

What is a common feature of sine and cosine regarding limits?

• They are undefined at pi

• They have limits equal to their function values at any point

• They are only defined for positive angles

• They have vertical asymptotes

What is the limit of cosine of x as x approaches pi/4?

• 1

• 0

• √2/2

• Undefined

What happens to the limit of tangent of x as x approaches pi?

• It is -1

• It is undefined

• It is 0

• It is 1

Why does the limit of tangent of x not exist as x approaches pi/2?

• Tangent is continuous at pi/2

• Cosine is one at pi/2

• Sine is zero at pi/2

• Tangent is not defined at pi/2

What is a key characteristic of tangent at pi/2?

• It is continuous

• It is zero

• It has a horizontal asymptote

• It has a vertical asymptote

What is the limit of cotangent of x as x approaches pi?

• 0

• -1

• Undefined

• 1

Why does the limit of cotangent of x not exist at pi?

• Cotangent is continuous at pi

• Cotangent is defined at pi

• Cotangent has a vertical asymptote at pi

• Cotangent is zero at pi

What is the relationship between cotangent and tangent?

• Cotangent is the integral of tangent

• Cotangent is the reciprocal of tangent

• Cotangent is the square of tangent

• Cotangent is the derivative of tangent