Continuity of Trigonometric Functions

The video discusses the continuity of trigonometric functions, focusing on sine, cosine, tangent, cotangent, secant, and cosecant. Sine and cosine are always continuous, while the others are only continuous within their domains. The video explains the proof of continuity for the tangent function and highlights the importance of understanding the domains where these functions are defined.

What is the main focus of the video tutorial?

• The integration of polynomial functions

• The continuity of trigonometric functions

• The differentiation of algebraic functions

• The properties of logarithmic functions

Which trigonometric functions are always defined?

• Tangent and cotangent

• Sine and cosine

• All trigonometric functions

• Secant and cosecant

What is the value of sine at zero?

• Undefined

• Zero

• Negative one

• One

Which of the following functions is not always defined?

• Sine

• Cosine

• All are always defined

• Tangent

What happens to the tangent function at 90 degrees?

• It is undefined

• It is one

• It is zero

• It is negative one

Why are some trigonometric functions not defined at certain points?

• Because they are always zero

• Because they are always negative

• Because their denominators become zero

• Because they are always one

What is the domain of the tangent function?

• All real numbers except where cosine is zero

• Only negative integers

• Only positive integers

• All real numbers

Which trigonometric functions are continuous everywhere?

• None of the above

• Secant and cosecant

• Sine and cosine

• Tangent and cotangent

What is the condition for the tangent function to be continuous?

• All trigonometric functions must be zero

• Tangent must be zero

• Sine must be zero

• Cosine must not be zero

Which functions are continuous only in their domains?

• Sine and cosine

• Tangent, cotangent, secant, and cosecant

• None of the trigonometric functions

• All trigonometric functions