Trigonometric Functions and Unit Circle

This video tutorial covers the concept of the unit circle, explaining its properties and how it is divided into four quadrants. It introduces the angles alpha and theta, detailing their relationships in each quadrant. The video also explores the trigonometric functions sine, cosine, and tangent, and how they relate to these angles in different quadrants. It provides a method for finding reference angles and demonstrates how to express trigonometric functions in terms of these reference angles through examples.

What is the center of a unit circle in a Cartesian plane?

• At the origin

• At (1,0)

• At (1,1)

• At (0,1)

What is the radius of a unit circle?

• 2 units

• 3 units

• 1 unit

• 0.5 units

In which direction are the quadrants of the unit circle numbered?

• Randomly

• Anti-clockwise

• Horizontally

• Clockwise

What is the acute angle between a line in a quadrant and the x-axis called?

• Gamma

• Alpha

• Beta

• Theta

In the first quadrant, how do alpha and theta relate?

• Alpha is theta plus 90 degrees

• Alpha equals theta

• Alpha is greater than theta

• Alpha is less than theta

In the second quadrant, what is the relationship between alpha and theta?

• Alpha equals theta

• Alpha plus theta equals 180 degrees

• Alpha is theta minus 180 degrees

• Alpha plus theta equals 360 degrees

In the third quadrant, how is alpha calculated from theta?

• Alpha equals theta

• Alpha is theta minus 180 degrees

• Alpha plus theta equals 180 degrees

• Alpha plus theta equals 360 degrees

In the fourth quadrant, what is the formula for alpha?

• Alpha is theta minus 180 degrees

• Alpha plus theta equals 180 degrees

• Alpha is 360 degrees minus theta

• Alpha equals theta

What does 'Add Sugar to Coffee' help determine?

• The positivity of trigonometric functions

• The color of the quadrants

• The size of the unit circle

• The position of the origin

In the first quadrant, which trigonometric functions are positive?

• Only cosine

• Only sine

• Only tangent

• All functions