Radians and Trigonometric Functions

The video tutorial by Colfax Math covers the differences between degrees and radians, explaining how to calculate radians and their origin. It discusses five problem types, including converting degrees to radians and vice versa, both as exact and approximate values. The tutorial emphasizes the unitless nature of radians and their application in various fields. It also covers solving trig functions using exact values, providing a comprehensive understanding of these mathematical concepts.

What is the difference between exact and approximate values in the context of radians?

• Exact values are only used in degrees, not radians.

• Exact values are expressed in terms of pi, while approximate values are decimal approximations.

• Exact values are always larger than approximate values.

• Exact values are calculated using a calculator, while approximate values are not.

Why are radians considered unitless?

• Because they are always less than one.

• Because they are always measured in degrees.

• Because the units cancel out when calculating the circumference to diameter ratio.

• Because they are only used in theoretical mathematics.

What is the equivalent of 180 degrees in radians?

• Pi

• 2 Pi

• Pi/2

• 3 Pi

How many radians are there in a full circle?

• Pi

• 2 Pi

• Pi/2

• 3 Pi

What is the first step in converting degrees to radians?

• Subtract 180

• Multiply by pi/180

• Multiply by 180/pi

• Add 180

When converting radians to degrees, what factor is used?

• 180/pi

• Pi/180

• Pi/360

• 360/pi

What is the sine of pi/3?

• Root 3/2

• 1

• 1/2

• Root 2/2

In a 30-60-90 triangle, what is the ratio of the side opposite the 60-degree angle?

• 2

• Root 3

• Root 2

• 1

What is the cosine of pi/3?

• 1/2

• Root 3/2

• Root 2/2

• 1

What is the exact value of 4 times the sine of pi/3 times the cosine of pi/3?

• Root 3

• 2

• 1

• Root 2