Trigonometric Functions and Unit Circle

This video tutorial by Mr. Backer explores trigonometric functions using the unit circle. It begins with an introduction to the unit circle, explaining its significance in connecting right triangle trigonometry with trigonometric functions. The video covers the basic trigonometric ratios: sine, cosine, and tangent, and their reciprocal functions: cosecant, secant, and cotangent. It also discusses the properties of the unit circle, including its coordinates and how they relate to trigonometric functions. Finally, the video delves into trigonometric identities, using the Pythagorean theorem to derive key relationships.

What is the radius of the unit circle?

• 3

• 2

• 1

• 0

Where is the unit circle centered?

• At (1,0)

• At (2,2)

• At (0,0)

• At (1,1)

What is the significance of the unit circle in trigonometry?

• It is used for drawing circles.

• It helps in calculating areas.

• It connects right triangle trigonometry with trigonometric functions.

• It is used for measuring angles.

What is the length of the hypotenuse in a right triangle formed in the unit circle?

• 0

• 1

• 2

• 3

In the unit circle, what does the x-coordinate of a point represent?

• The cosecant of the angle

• The tangent of the angle

• The cosine of the angle

• The sine of the angle

In the unit circle, what does the y-coordinate of a point represent?

• The tangent of the angle

• The cosine of the angle

• The sine of the angle

• The secant of the angle

What is the x-coordinate of the point where the unit circle intersects the positive x-axis?

• 0

• -1

• 2

• 1

What is the y-coordinate of the point where the unit circle intersects the positive y-axis?

• 2

• -1

• 1

• 0

What is the x-coordinate of the point where the unit circle intersects the negative x-axis?

• 0

• 2

• -1

• 1

What is the y-coordinate of the point where the unit circle intersects the negative y-axis?

• 2

• -1

• 1

• 0