Trigonometric Functions and Radians

The video tutorial explains how to find exact trigonometric function values using reference triangles. It covers the conversion of angles from radians to degrees and emphasizes the importance of understanding radians. The tutorial includes detailed steps for sketching angles in standard position, forming reference triangles, and calculating sine and cosine values for angles 7π/4 and -3π/4 radians. It also discusses rationalizing denominators and provides notes on the 45-45-90 reference triangle.

Why is it important to learn how to work with radians instead of just converting to degrees?

• Radians are more precise than degrees.

• Radians are the standard unit in calculus.

• Degrees are not used in trigonometry.

• Radians are easier to calculate.

What is the reference angle for 7π/4 radians?

• π radians

• π/4 radians

• 3π/4 radians

• π/2 radians

In which quadrant is the angle 7π/4 radians located?

• First quadrant

• Fourth quadrant

• Second quadrant

• Third quadrant

What is the sine of 7π/4 radians when rationalized?

• √2/2

• 1/√2

• -√2/2

• -1/√2

What is the cosine of 7π/4 radians when rationalized?

• 1/√2

• -√2/2

• √2/2

• -1/√2

How do you determine the reference angle for a negative angle like -3π/4 radians?

• Subtract 2π radians

• Add 2π radians

• Subtract π/4 radians

• Add π/4 radians

In which quadrant is the angle -3π/4 radians located?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the sine of -3π/4 radians when rationalized?

• -1/√2

• √2/2

• -√2/2

• 1/√2

What is the cosine of -3π/4 radians when rationalized?

• -√2/2

• 1/√2

• √2/2

• -1/√2

What is a key characteristic of a 45-45-90 triangle?

• All sides are equal.

• The legs are equal, and the hypotenuse is √2 times a leg.

• The hypotenuse is equal to a leg.

• The hypotenuse is twice the length of a leg.