Sine Function and Unit Circle Concepts

The video tutorial explains how to solve the equation sine x equals negative square root two divided by two for all solutions in degrees. It begins by identifying where the sine function is negative on the coordinate plane, specifically in the third and fourth quadrants. The reference angle with a sine value of square root two divided by two is determined to be 45 degrees. The tutorial then finds coterminal angles in the third and fourth quadrants, resulting in solutions of x equals 225 plus 360k degrees and x equals 315 plus 360k degrees. These solutions are verified using the unit circle and graphically with a sine graph, showing infinite points of intersection.

In which quadrants is the sine function negative?

• First and Fourth

• Second and Third

• Third and Fourth

• First and Second

What is the reference angle for a sine value of square root two divided by two?

• 90 degrees

• 30 degrees

• 45 degrees

• 60 degrees

What is the least positive angle in the third quadrant with a sine value of negative square root two divided by two?

• 225 degrees

• 135 degrees

• 315 degrees

• 405 degrees

How do you find all coterminal angles to a given angle?

• Add multiples of 180 degrees

• Add multiples of 270 degrees

• Add multiples of 90 degrees

• Add multiples of 360 degrees

What is the least positive angle in the fourth quadrant with a sine value of negative square root two divided by two?

• 405 degrees

• 225 degrees

• 315 degrees

• 135 degrees

On the unit circle, what does the sine of an angle represent?

• The y-coordinate

• The x-coordinate

• The radius

• The angle itself

Which angles on the unit circle have a y-coordinate of negative square root two divided by two?

• 45 and 135 degrees

• 225 and 315 degrees

• 135 and 225 degrees

• 315 and 405 degrees

What does the graphical representation of y = sine x and y = negative square root two divided by two show?

• An infinite number of points of intersection

• Two points of intersection

• No points of intersection

• A single point of intersection

What is the next angle after 225 degrees that has the same sine value?

• 315 degrees

• 405 degrees

• 585 degrees

• 675 degrees

What is the next angle after 315 degrees that has the same sine value?

• 765 degrees

• 675 degrees

• 495 degrees

• 405 degrees