Trigonometric Functions and Unit Circle

The video tutorial introduces the concept of the unit circle, explaining its properties and significance in trigonometry. It covers the calculation of ordered pairs using special right triangles and explores angles in different quadrants. The tutorial introduces trigonometric ratios, including sine, cosine, and tangent, and explains the mnemonic SOHCAHTOA to remember these ratios. The video aims to provide foundational knowledge for understanding trigonometry and its applications in calculus.

What is the radius of a unit circle?

• 0

• 1

• 2

• 3

Which of the following is an ordered pair on the x-axis of the unit circle?

• (0, 1)

• (1, 0)

• (-1, 0)

• (0, -1)

In a 30-60-90 triangle, what is the length of the hypotenuse if the short leg is 0.5?

• 2

• 1.5

• 1

• 0.5

What is the x-coordinate of a point at a 45-degree angle on the unit circle?

• √2/2

• 0.5

• √3/2

• 1

In which quadrant are both x and y coordinates negative?

• First

• Fourth

• Second

• Third

What is the sine of an angle in a right triangle?

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Adjacent over opposite

• Hypotenuse over opposite

What does the acronym SOHCAHTOA help you remember?

• Quadrant signs

• Unit circle properties

• Trigonometric ratios

• Trigonometric identities

What is the cosine of 30 degrees on the unit circle?

• 1

• 1/2

• √2/2

• √3/2