Understanding Trigonometric Functions on the Unit Circle

The video tutorial explores the unit circle and its relationship with sine and cosine. It begins by explaining how the unit circle helps determine the sine and cosine of an angle theta. The tutorial then connects the unit circle definition to the traditional Soh Cah Toa definition of trigonometry. Finally, it explores the relationship between sine and cosine when the angle is increased by pi over two, demonstrating how these concepts are interconnected.

What does the X coordinate of the terminal ray on the unit circle represent?

• Cotangent of theta

• Cosine of theta

• Sine of theta

• Tangent of theta

According to the unit circle definition, what is the sine of theta?

• The length of the adjacent side

• The X coordinate

• The length of the hypotenuse

• The Y coordinate

How does the unit circle definition extend the Soh Cah Toa definition?

• By using a different hypotenuse

• By changing the angle measurement

• By considering the unit circle's radius as the hypotenuse

• By altering the opposite side

What is the equivalent of pi over two radians in degrees?

• 45 degrees

• 180 degrees

• 60 degrees

• 90 degrees

What happens to the terminal side of an angle when pi over two is added?

• It becomes parallel to the X-axis

• It remains unchanged

• It rotates 90 degrees counterclockwise

• It rotates 90 degrees clockwise

What is the relationship between cosine of theta and sine of theta plus pi over two?

• Cosine of theta is equal to sine of theta plus pi over two

• Cosine of theta is unrelated to sine of theta plus pi over two

• Cosine of theta is double sine of theta plus pi over two

• Cosine of theta is half sine of theta plus pi over two

What is the sine of theta plus pi over two in terms of the unit circle?

• The length of the hypotenuse

• The Y coordinate

• The X coordinate

• The length of the adjacent side

What should you explore after understanding the relationship between sine and cosine?

• The relationship between tangent and cotangent

• The relationship between sine and cosine for other angles

• The relationship between secant and cosecant

• The relationship between angles and their complements

What might cosine of theta plus pi over two relate to?

• Cosine of theta

• Cotangent of theta

• Tangent of theta

• Sine of theta

What is encouraged for further exploration in trigonometry?

• Exploring the relationship between tangent and cotangent

• Exploring the relationship between secant and cosecant

• Exploring the relationship between sine and cosine for different angles

• Exploring the relationship between angles and their supplements