Understanding Tangent Function Solutions

The video tutorial explains how to solve the equation tangent x equals one for all solutions, using degrees and integer k. It first uses reference triangles to find solutions, then verifies them using the unit circle and graphically. The tangent function's positive value is explored in the first and third quadrants, with reference angles of 45 and 225 degrees. The period of the tangent function is 180 degrees, simplifying the expression of solutions. The unit circle confirms the solutions, and graphical representation shows infinite intersections, verifying the correctness of the solutions.

What is the primary method used to solve the equation tangent x equals one?

• Using reference triangles

• Using logarithms

• Using algebraic manipulation

• Using calculus

In which quadrants is the tangent function positive?

• Second and third

• First and third

• First and second

• Second and fourth

What is the reference angle that gives a tangent value of one?

• 60 degrees

• 90 degrees

• 45 degrees

• 30 degrees

How do you find coterminal angles for a given angle?

• Add or subtract multiples of 90 degrees

• Add or subtract multiples of 45 degrees

• Add or subtract multiples of 180 degrees

• Add or subtract multiples of 360 degrees

What is the simplified expression for all solutions of tangent x equals one?

• x = 45 + 90k

• x = 45 + 180k

• x = 45 + 360k

• x = 45 + 270k

What is the period of the tangent function?

• 360 degrees

• 90 degrees

• 180 degrees

• 270 degrees

On the unit circle, at which angles do x and y have equal values?

• 90 and 270 degrees

• 45 and 225 degrees

• 60 and 240 degrees

• 30 and 150 degrees

What does the graph of y = tangent x intersect with to find solutions?

• y = 1

• y = 0

• y = x

• y = -1

How can you verify the solutions graphically?

• By measuring the angle with a protractor

• By finding the points of intersection with y = 1

• By checking the slope of the tangent line

• By using a calculator

What happens when you add multiples of 180 degrees to 45 degrees?

• You get angles in the first quadrant

• You get angles in the fourth quadrant

• You get angles in the second quadrant

• You get angles coterminal to 45 degrees