Trigonometric Functions and Asymptotes

The video tutorial explores conceptual questions about trigonometric graphs and inverse trigonometric properties. It explains why asymptotes exist for cotangent and tangent functions but not for sine and cosine, using the unit circle as a reference. The tutorial highlights that asymptotes occur where functions are undefined, particularly when the denominator equals zero. It identifies specific points on the unit circle where tangent and cotangent are undefined, leading to asymptotes.

What is the main focus of the video tutorial?

• Conceptual questions about algebra

• Conceptual questions about trigonometric graphs and inverse trig properties

• Conceptual questions about calculus

• Conceptual questions about geometry

Why do tangent and cotangent functions have asymptotes?

• Because they are linear functions

• Because they have a denominator of zero

• Because they are quadratic functions

• Because they have a numerator of zero

What is the radius of the unit circle?

• 3

• 0

• 2

• 1

In the unit circle, what does sine of theta represent?

• Angle

• Radius

• Y-coordinate

• X-coordinate

What is the condition for a tangent function to have an asymptote?

• When the numerator is zero

• When the function is quadratic

• When the function is linear

• When the denominator is zero

At which angles does tangent have asymptotes on the unit circle?

• 0 and π

• π/6 and 5π/6

• π/2 and 3π/2

• π/4 and 3π/4

What is the formula for cotangent of theta?

• Y/X

• Y*X

• X/Y

• X*Y

Where does cotangent have asymptotes on the unit circle?

• Where x = 0

• Where y = 0

• Where x = y

• Where x = -y

Why don't sine and cosine have asymptotes?

• Because they are quadratic

• Because they are linear

• Because they have no denominator

• Because they are undefined

What happens to the graph of a function at an asymptote?

• It becomes a straight line

• It becomes a circle

• It becomes a parabola

• It becomes undefined