Unit Circle and Tangent Functions

The video tutorial explains the unit circle's role in defining sine and cosine, moving beyond triangles. It highlights the tangent's unique relationship with the unit circle, explaining why it's called 'tangent' and how it relates to angles. The tutorial covers calculating tangent values for various angles and discusses when tangent becomes undefined, providing a comprehensive understanding of these trigonometric concepts.

What is the primary purpose of the unit circle in trigonometry?

• To measure the circumference of circles

• To calculate the area of circles

• To redefine sine and cosine for angles greater than 180 degrees

• To define angles in triangles

How is the tangent of an angle derived from sine and cosine?

• By dividing sine by cosine

• By multiplying sine and cosine

• By subtracting cosine from sine

• By adding sine and cosine

Why is tangent called 'tangent' in relation to the unit circle?

• Because it is a line that touches the circle at one point

• Because it is parallel to the radius

• Because it is perpendicular to the radius

• Because it is a line inside the circle

What happens to the tangent line as the angle increases?

• It becomes shorter

• It disappears

• It becomes longer

• It remains the same length

What is the exact value of tan(45 degrees) or tan(pi/4)?

• 0

• 1

• √2

• Undefined

What is the approximate value of tan(pi/3)?

• 1

• √3

• 0.5

• Undefined

Why is tan(pi/2) undefined?

• Because the sine and cosine are equal

• Because the tangent line is too short

• Because the tangent line never meets the radius

• Because the angle is too small

What is the x-coordinate of a point on the unit circle?

• Cosine of the angle

• Radius of the circle

• Sine of the angle

• Tangent of the angle

What is the y-coordinate of a point on the unit circle?

• Sine of the angle

• Cosine of the angle

• Tangent of the angle

• Radius of the circle

What does the tangent of an angle represent in the unit circle?

• The x-coordinate

• The y-coordinate

• The radius of the circle

• The length of the tangent line