Trigonometric Functions and Identities

This video tutorial covers trigonometric functions and their relationship with the unit circle. It explains how to evaluate sine and cosine using reference triangles, including for negative angles. The tutorial also explores Pythagorean identities and their application in trigonometry. Additionally, it discusses tangent and coterminal angles, and how to evaluate secant, cosecant, and cotangent for specific angles.

What is the primary relationship between the unit circle and trigonometric functions?

• The unit circle is unrelated to trigonometric functions.

• The unit circle helps in visualizing angles and their trigonometric values.

• The unit circle is used to measure angles in radians only.

• The unit circle defines the radius of all triangles.

What are the sine and cosine values for the angle 2π/3?

• Sine: √3/2, Cosine: 1/2

• Sine: -1/2, Cosine: √3/2

• Sine: √3/2, Cosine: -1/2

• Sine: 1/2, Cosine: √3/2

In which quadrant is the angle 2π/3 located?

• Second Quadrant

• Third Quadrant

• First Quadrant

• Fourth Quadrant

What is the cosine of a negative 45-degree angle?

• √2/2

• -√2/2

• 1

• -1

How do you convert a negative angle to a positive angle on the unit circle?

• Add 360 degrees

• Subtract 360 degrees

• Add 180 degrees

• Subtract 180 degrees

What is the Pythagorean identity involving sine and cosine?

• sine^2 - cosine^2 = 0

• sine^2 + cosine^2 = 0

• sine^2 - cosine^2 = 1

• sine^2 + cosine^2 = 1

If cosine of an angle in the third quadrant is -3/5, what is the sine?

• -3/5

• -4/5

• 4/5

• 3/5

What is the tangent of negative 5π/6?

• 1/√3

• -1/√3

• -√3

• √3

What is the tangent of 3π?

• -1

• 0

• 1

• Undefined

What is the secant of a 135-degree angle?

• -√2

• 2

• √2

• -2