Cosine Values and Quadrants

The video tutorial explains how to solve the equation cosine x equals negative one-half for all solutions in degrees. It uses reference triangles and the unit circle to determine where cosine is negative, focusing on the second and third quadrants. The tutorial demonstrates how to find reference angles and calculate coterminal angles, providing solutions in the form of x equals 120 plus 360k degrees and x equals 240 plus 360k degrees. Verification is done using the unit circle and graphically, showing the infinite number of solutions due to the periodic nature of the cosine function.

In which quadrants is the cosine function negative?

• First and Fourth

• Third and Fourth

• Second and Third

• First and Second

What is the reference angle for a cosine value of one-half?

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

What is the cosine of 60 degrees?

• 1

• -1/2

• 0

• 1/2

What is the least positive angle in the second quadrant with a cosine of negative one-half?

• 90 degrees

• 180 degrees

• 150 degrees

• 120 degrees

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

• Add or subtract multiples of 180 degrees

• Add or subtract multiples of 270 degrees

• Add or subtract multiples of 360 degrees

• Add or subtract multiples of 90 degrees

What is the least positive angle in the third quadrant with a cosine of negative one-half?

• 180 degrees

• 240 degrees

• 270 degrees

• 210 degrees

On the unit circle, where is the cosine value negative?

• First and Fourth quadrants

• First and Second quadrants

• Second and Third quadrants

• Third and Fourth quadrants

What is the x-coordinate for cosine in the second quadrant for a value of negative one-half?

• -1/2

• -1

• 0

• 1/2

What does the graph of y = cosine x and y = -1/2 show about the solutions?

• There are infinite solutions

• There is one solution

• There are no solutions

• There are two solutions

What is the next angle after 240 degrees that also has a cosine of negative one-half?

• 600 degrees

• 360 degrees

• 300 degrees

• 480 degrees