Limits and Trigonometric Functions

The video tutorial revisits the concept of limits, focusing on the special case where the limit equals one, and its implications in trigonometry. The teacher explains the relationship between sine, tangent, and cosine as theta approaches zero, emphasizing the product of limits. Graphical representations and inequalities are used to illustrate these concepts, leading to a discussion on algebraic applications.

What makes the number one special in the context of limits discussed in the video?

• It is the smallest positive number.

• It is the largest integer.

• It is its own reciprocal.

• It is the only even prime number.

How can sine be expressed in terms of tangent and cosine as theta approaches zero?

• Sine equals tangent divided by cosine.

• Sine equals cosine minus tangent.

• Sine equals tangent times cosine.

• Sine equals cosine divided by tangent.

What is the behavior of cosine as theta approaches zero?

• It approaches one.

• It approaches negative one.

• It becomes undefined.

• It approaches zero.

Why is it important to indicate multiplication by one in limit calculations?

• To demonstrate understanding of the limit process.

• To change the value of the limit.

• To show that the term is ignored.

• To make the calculation more complex.

What is the limit of tangent over theta as theta approaches zero?

• One

• Infinity

• Negative one

• Zero

In the first quadrant, how do sine, theta, and tangent behave as they approach the origin?

• They remain constant.

• They converge towards each other.

• They oscillate.

• They diverge from each other.

What is the concavity of the sine function as it approaches the origin?

• Concave up

• Concave down

• Oscillating

• Linear

What does the inequality involving sine, theta, and tangent represent geometrically?

• A hexagon inside a circle

• A rectangle inside a circle

• A triangle inside a circle

• A square inside a circle

Which function is always in the middle according to the inequality discussed?

• Tangent

• Theta

• Cosine

• Sine

What is the significance of the inequality when theta is acute?

• It shows that tangent is always below sine.

• It shows that sine is always above theta.

• It shows that theta is always between sine and tangent.

• It shows that cosine is always above tangent.