Evaluating for cosine using coterminal angles

The video tutorial explains how to evaluate trigonometric functions using the smallest positive or negative coterminal angles. It demonstrates the process of finding coterminal angles by adding or subtracting 2π, and simplifies the angle -9π/4 to -π/4. The tutorial further explains how to evaluate the cosine of the simplified angle, considering the coordinate points and quadrants involved.

Why is it important to use the smallest positive or negative coterminal angles when evaluating trigonometric functions?

• To simplify calculations and avoid large numbers

• To ensure the angle is always positive

• To make the angle a multiple of π

• To avoid using fractions

What is the reason for adding 2π instead of subtracting it when dealing with a negative angle greater than 2π?

• Adding 2π makes the angle positive

• Subtracting 2π would increase the negative value

• Adding 2π changes the angle to a sine function

• Subtracting 2π is not mathematically valid

How can 2π be expressed as a fraction with a denominator of 4?

• 2π = 10π/4

• 2π = 8π/4

• 2π = 6π/4

• 2π = 4π/2

What is the cosine value of the angle -π/4?

• -sqrt(2)/2

• sqrt(2)/2

• 1

• 0

In which quadrant does the angle -π/4 lie, and what is the significance of the x-coordinate in this context?

• First quadrant; x-coordinate is positive

• Second quadrant; x-coordinate is negative

• Third quadrant; x-coordinate is zero

• Fourth quadrant; x-coordinate determines cosine value