Understanding Cotangent Equation Solutions

The video tutorial explains how to solve the equation cotangent x = √3 for all solutions in degrees. It uses reference triangles and the unit circle to find solutions, focusing on when the cotangent function is positive. The tutorial identifies the reference angle and sketches reference triangles in relevant quadrants. It calculates solutions and coterminal angles, then simplifies the expression using the cotangent period. Finally, it verifies solutions on the unit circle and graphically, confirming the solution pattern.

What is the equation we are trying to solve in this tutorial?

• cotangent x equals 2

• cotangent x equals square root three

• cotangent x equals 1

• cotangent x equals zero

Tags

CCSS.HSF.TF.A.2

In which quadrants is the cotangent function positive?

• Second and fourth quadrants

• First and third quadrants

• Second and third quadrants

• First and second quadrants

Tags

CCSS.HSF.TF.A.2

What reference angle gives a cotangent value of square root three?

• 30 degrees

• 90 degrees

• 60 degrees

• 45 degrees

Tags

CCSS.HSF.TF.B.7

What is the least positive angle in the first quadrant for this equation?

• 60 degrees

• 90 degrees

• 45 degrees

• 30 degrees

How do you find coterminal angles?

• Add multiples of 45 degrees

• Add multiples of 90 degrees

• Add multiples of 360 degrees

• Add multiples of 180 degrees

Tags

CCSS.HSF.TF.B.7

What is the simplified expression for all solutions of the equation?

• x = 30 + 90k

• x = 30 + 360k

• x = 30 + 45k

• x = 30 + 180k

What is the period of the cotangent function?

• 90 degrees

• 180 degrees

• 360 degrees

• 45 degrees

Tags

CCSS.HSF.TF.A.2

How is the cotangent value verified on the unit circle?

• By checking the ratio of x to y

• By checking the hypotenuse

• By checking the y-coordinate

• By checking the x-coordinate

Tags

CCSS.HSF.TF.B.7

What is the graphical representation of the solution?

• Intersection of y = cotangent x and y = 1

• Intersection of y = cotangent x and y = 2

• Intersection of y = cotangent x and y = square root of three

• Intersection of y = cotangent x and y = 0

Tags

CCSS.HSF.TF.B.7

What happens if you keep adding 180 degrees to the angle?

• You find solutions only in the first quadrant

• You find more solutions in the negative direction

• You find more solutions in the positive direction

• You find no additional solutions

Tags

CCSS.HSF.TF.B.7