Understanding Limits in Trigonometric Functions

The video tutorial explains how to determine limits for trigonometric functions like cosine, sine, and tangent as x approaches specific values. It covers the domain and continuity of these functions, using direct substitution and reference triangles to find limits. The tutorial also discusses the behavior of the tangent function near vertical asymptotes, concluding that the limit does not exist in such cases.

What is the domain of the cosine function?

• Only integers

• Only negative numbers

• Only positive numbers

• All real numbers

How can the limit of cosine x as x approaches pi/4 be determined?

• By guessing

• By direct substitution

• By using a calculator

• By using a logarithm

What is the value of cosine pi/4?

• Square root of 2 divided by 2

• 0

• Square root of 3 divided by 2

• 1

What is the domain of the sine function?

• Only negative numbers

• Only integers

• Only positive numbers

• All real numbers

What is the value of sine pi/6?

• 1/2

• Square root of 3 divided by 2

• 0

• 1

What is the larger acute angle in a 30-60-90 triangle?

• Pi over 4

• Pi over 2

• Pi over 6

• Pi over 3

What is the y-coordinate of the terminal side of pi/6 on the unit circle?

• 1/2

• 0

• Square root of 3 divided by 2

• 1

What is the domain of the tangent function?

• All real numbers except odd multiples of pi/2

• Only positive numbers

• Only integers

• All real numbers

What happens to the tangent function as x approaches pi/2?

• It oscillates

• It approaches infinity

• It remains constant

• It approaches zero

Does the limit of tangent x as x approaches pi/2 exist?

• Yes, it is zero

• Yes, it is infinity

• No, it does not exist

• Yes, it is one