Understanding Cotangent Solutions

The video tutorial explains how to solve the equation cotangent x equals negative square root three divided by three for all solutions in exact radian form. It uses reference triangles and the unit circle to determine the solutions, focusing on the second and fourth quadrants where the cotangent function is negative. The tutorial simplifies the solution by recognizing the period of the cotangent function and verifies the solutions graphically.

What is the value of cotangent x that we are trying to solve for?

• Square root three

• Negative square root three

• Square root three divided by three

• Negative square root three divided by three

In which quadrants will the solutions for cotangent x be located?

• First and third quadrants

• Second and third quadrants

• Second and fourth quadrants

• First and fourth quadrants

What is the reference angle for cotangent x when rationalized?

• Pi over six

• Pi over four

• Pi over three

• Pi over two

What is the adjacent side length in the second quadrant reference triangle?

• Square root three

• Negative one

• Negative square root three

• Positive one

What is the least positive angle in the second quadrant that satisfies the equation?

• Two-thirds pi

• Pi

• Five-thirds pi

• Pi over two

How do we express all solutions for the angle in the second quadrant?

• Add multiples of pi

• Add multiples of two pi

• Subtract multiples of pi

• Subtract multiples of two pi

What is the period of the cotangent function?

• Pi radians

• Two pi radians

• Three pi radians

• Four pi radians

How can we verify the solution using the unit circle?

• By checking the ratio of x to y

• By checking the hypotenuse

• By checking the y-coordinates

• By checking the x-coordinates

What does the graph of y equals cotangent x intersect with to verify solutions?

• y equals zero

• y equals one

• y equals negative square root three divided by three

• y equals square root three

What happens to the solutions if we subtract pi radians from two-thirds pi?

• We get positive solutions

• We get negative solutions

• We get zero

• We get undefined