Understanding Tangent and Angle Relationships

The video explores the concept of tangent in trigonometry, focusing on its relationship with sine and cosine. It explains how the tangent of an angle is the slope of the terminal ray and examines the properties of tangent for angles like theta plus pi, negative theta, and pi minus theta. The video highlights the symmetry in the unit circle and how these properties can be useful in solving trigonometric problems and proving identities.

What is the tangent of an angle defined as in terms of sine and cosine?

• Cosine minus sine

• Sine times cosine

• Sine over cosine

• Cosine over sine

How does the tangent of an angle relate to the slope of its terminal ray?

• It is the square

• It is the slope

• It is the inverse

• It is unrelated

Which of the following angles will have the same tangent as theta?

• Pi minus theta

• Negative theta

• Theta minus pi

• Theta plus pi

What is the relationship between the tangent of theta and the tangent of theta plus pi?

• They are opposites

• They are equal

• One is half the other

• One is double the other

What happens to the tangent of an angle when the angle is negated?

• It doubles

• It becomes positive

• It becomes negative

• It remains the same

Which of the following is true about the tangent of negative theta?

• It equals the sine of theta

• It equals the cosine of theta

• It equals the negative tangent of theta

• It equals the tangent of theta

How does the tangent of pi minus theta compare to the tangent of theta?

• It is the same

• It is double

• It is the negative

• It is half

What does the tangent of pi minus theta equal?

• Sine of theta

• Cosine of theta

• Negative tangent of theta

• Tangent of theta

What is the significance of adding pi to an angle in terms of its tangent?

• The tangent becomes zero

• The tangent remains unchanged

• The tangent becomes negative

• The tangent doubles

What is the effect of adding pi to an angle on its tangent?

• The tangent becomes zero

• The tangent remains the same

• The tangent becomes negative

• The tangent doubles