Solving Trigonometric Equations

The video tutorial explains how to solve the equation sine x equals negative square root of three divided by two for all solutions, using exact radian answers. It covers the use of reference triangles and the unit circle to find solutions in the third and fourth quadrants. The tutorial also discusses finding coterminal angles and verifies the solutions using both the unit circle and graphical methods. The process involves identifying reference angles, calculating coterminal angles, and confirming the results through visual representation on a graph.

In which quadrants is the sine function negative?

• Third and Fourth

• Second and Third

• First and Fourth

• First and Second

What is the reference angle for a sine value of √3/2?

• π/4

• π/3

• π/6

• π/2

What is the least positive angle in the third quadrant for sin(x) = -√3/2?

• π/3

• 2π/3

• 4π/3

• 5π/3

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

• Add multiples of π

• Add multiples of 2π

• Subtract multiples of π

• Subtract multiples of 2π

What is the y-coordinate on the unit circle for sin(x) = -√3/2?

• √3/2

• -√3/2

• -1/2

• 1/2

Which angles on the unit circle correspond to sin(x) = -√3/2?

• π/3 and 2π/3

• 4π/3 and 5π/3

• π/6 and 5π/6

• π/4 and 3π/4

What does the graph of y = sin(x) intersecting y = -√3/2 indicate?

• Finite solutions

• Infinite solutions

• No solutions

• Single solution

What is the next angle after 4π/3 that satisfies sin(x) = -√3/2?

• 16π/3

• 5π/3

• 10π/3

• 8π/3

How can you verify trigonometric solutions graphically?

• By checking intersections with a vertical line

• By checking intersections with a horizontal line

• By checking intersections with the y-axis

• By checking intersections with the x-axis

What is the significance of adding or subtracting multiples of 2π?

• It changes the angle's cosine value

• It changes the angle's quadrant

• It finds coterminal angles

• It changes the angle's sine value