Trigonometric Functions and Unit Circle

This video tutorial covers the unit circle, including its quadrants and the conversion between degrees and radians. It explains how to use the unit circle to evaluate trigonometric functions and introduces special triangles like the 30-60-90 and 45-45-90 triangles. The tutorial also explores inverse trigonometric functions, their domains, and techniques for solving trigonometric problems. Advanced concepts such as double angles and trigonometric identities are discussed, providing a comprehensive overview of trigonometry.

In which quadrant are all trigonometric functions positive?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

What is the radian measure of 180 degrees?

• 3π/2

• π/2

• π

• 2π

What are the coordinates of 90 degrees on the unit circle?

• (1, 0)

• (0, -1)

• (0, 1)

• (-1, 0)

In which quadrant is the x-coordinate negative and the y-coordinate positive?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What is the sine of 60 degrees using the unit circle?

• √2/2

• √3/2

• 1/2

• 0

How do you find the reference angle for an angle in Quadrant III?

• Subtract 180 from the angle

• Subtract the angle from 180

• Subtract the angle from 360

• Subtract 360 from the angle

What is the cosine of 45 degrees using a 45-45-90 triangle?

• 1

• √3/2

• √2/2

• 1/2

What is the tangent of 30 degrees using a 30-60-90 triangle?

• √3

• 1/√3

• 1

• √3/3

In which quadrants does the inverse sine function exist?

• Quadrants III and IV

• Quadrants II and III

• Quadrants I and IV

• Quadrants I and II

What is the inverse cosine of 1/2?

• 120 degrees

• 30 degrees

• 90 degrees

• 60 degrees