Trigonometric Functions and Unit Circle

The video tutorial explains the relationship between the unit circle and trigonometric functions. It begins with a recap of the unit circle and introduces the concept of associating angles with points on the circle. The tutorial then demonstrates how to calculate cosine and sine using the unit circle, extending these definitions to angles beyond acute angles. The video concludes with examples illustrating the application of these concepts to find all six trigonometric functions for given points on the unit circle.

What is the significance of the unit circle in extending trigonometric functions?

• It limits trigonometric functions to acute angles

• It allows defining trigonometric functions for any angle

• It only applies to angles in the first quadrant

• It is used to calculate the area of a circle

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

• To calculate areas of circles

• To define trigonometric functions for all angles

• To measure angles in radians

• To find the circumference of a circle

What does it mean for an angle to be in standard position?

• It is measured in degrees

• Its vertex is at the origin and initial side on the positive x-axis

• It is always acute

• It is measured in radians

How is cosine of an angle defined in a right triangle?

• Opposite side divided by hypotenuse

• Adjacent side divided by hypotenuse

• Hypotenuse divided by opposite side

• Hypotenuse divided by adjacent side

How is the tangent of an angle defined using the unit circle?

• Opposite side divided by adjacent side

• Adjacent side divided by opposite side

• Cosine divided by sine

• Sine divided by cosine

What is the cosine of an angle associated with the point (-1/2, √3/2) on the unit circle?

• -1/2

• 1/2

• √3/2

• -√3/2

For a point (2/3, -√5/3) on the unit circle, what is the sine of the associated angle?

• 2/3

• -2/3

• -√5/3

• √5/3