Understanding Tangent Function Solutions

The video tutorial explains how to solve the equation tangent x = -1 for all solutions, providing exact radian answers. It uses reference triangles and verifies solutions using the unit circle and graphically. The process involves recognizing the negative tangent value, finding reference angles, determining all solutions using coterminal angles, and verifying these solutions with the unit circle and graph. The tutorial emphasizes the periodic nature of the tangent function and provides a simplified expression for all solutions.

What is the first step in solving the equation tangent x equals negative one?

• Sketch the unit circle.

• Find the reference angle with a tangent value of one.

• Recognize the negativity of the tangent function.

• Identify the period of the tangent function.

In which quadrants will the solutions for tangent x equals negative one be found?

• First and third quadrants

• Second and fourth quadrants

• Second and third quadrants

• First and fourth quadrants

What reference angle gives a tangent function value of positive one?

• Pi over 2 radians

• Pi radians

• Pi over 4 radians

• 3 Pi over 4 radians

What is the least positive angle in the second quadrant for the equation tangent x equals negative one?

• Pi over 2 radians

• 3 Pi over 4 radians

• Pi radians

• 5 Pi over 4 radians

How can all solutions for tangent x equals negative one be expressed?

• x = 3/4 Pi + 2 Pi k

• x = 3/4 Pi + Pi k

• x = Pi + 2 Pi k

• x = Pi/2 + Pi k

What is the least positive angle in the fourth quadrant for the equation tangent x equals negative one?

• Pi radians

• 5 Pi over 4 radians

• 7 Pi over 4 radians

• Pi over 2 radians

How is the tangent function's period used to simplify the expression for all solutions?

• By adding 2 Pi to the initial angle

• By subtracting 2 Pi from the initial angle

• By subtracting Pi from the initial angle

• By adding Pi to the initial angle

What must be true about x and y coordinates on the unit circle for tangent theta to equal negative one?

• y must be zero

• x and y must be equal

• x and y must be opposites

• x must be zero

How does the graph of y = tangent x help verify the solutions?

• By illustrating the unit circle

• By displaying the points of intersection with y = -1

• By showing the period of the tangent function

• By highlighting the reference angles

What is the next solution after 7/4 Pi radians when adding Pi radians?

• 11/4 Pi radians

• 15/4 Pi radians

• 9/4 Pi radians

• 13/4 Pi radians