Understanding Limits and Trigonometric Functions

The video tutorial explains how to determine limits using trigonometric functions like sine, cosine, and tangent. It demonstrates the process of direct substitution and simplification of expressions using the unit circle. The tutorial covers calculating limits as x approaches specific values, such as pi over six and pi over four, and emphasizes the continuity of trigonometric and linear functions over real numbers.

What is the first step in determining the limit of a function involving sine?

• Use the unit circle

• Perform direct substitution

• Apply L'Hôpital's rule

• Use a calculator

What is the sine of pi over six?

• Square root of 3 over 2

• 0

• 1

• 1/2

How do you simplify the expression 2/6 pi?

• 1/4 pi

• 1/2 pi

• 1/3 pi

• 1/6 pi

What is the least common denominator when adding 1/3 pi and 1/2 pi?

• 6

• 5

• 4

• 3

What is the sine of 5/6 pi?

• 1

• 0

• 1/2

• Square root of 3 over 2

What is the tangent of pi over four?

• Square root of 2

• 1

• 0

• Square root of 3

What is the least common denominator when adding 3/4 pi and 1/2 pi?

• 2

• 3

• 4

• 5

What is the cosine of 5/4 pi?

• 1

• Square root of 2 over 2

• Negative square root of 2 over 2

• 0

What is the result of multiplying 5 by negative square root of 2 divided by 2?

• Negative 5 square root of 2 divided by 2

• 5 square root of 2 divided by 2

• Negative 5 divided by 2

• 5 divided by 2

What is the cosine of pi over four?

• Square root of 2 over 2

• 1/2

• 0

• 1