Trigonometric Functions and Equations

The video tutorial explains how to solve a trigonometric equation over a given interval. It begins by introducing the equation and demonstrating how to factor it using substitution. The tutorial then solves for sine x and identifies the solutions on the unit circle. Finally, it concludes by summarizing the solutions found for the equation.

What substitution is used to simplify the given trigonometric equation?

• u = cos(x)

• u = cot(x)

• u = tan(x)

• u = sin(x)

What is the factored form of the equation 2u^2 - u - 1 = 0?

• (2u + 1)(u - 1)

• (2u - 1)(u + 1)

• (2u + 1)(u + 1)

• (2u - 1)(u - 1)

What are the possible values of sin(x) after factoring the equation?

• sin(x) = -1/2 or sin(x) = 1

• sin(x) = 1/2 or sin(x) = -1

• sin(x) = -1 or sin(x) = 0

• sin(x) = 0 or sin(x) = 1

In which quadrants is the sine function negative?

• Second and Third

• First and Fourth

• Third and Fourth

• First and Second

What is the angle in radians for sin(x) = -1/2 in the third quadrant?

• 11/6 π

• 7/6 π

• 2/3 π

• 5/6 π

What is the angle in radians for sin(x) = -1/2 in the fourth quadrant?

• 2/3 π

• 11/6 π

• 7/6 π

• 5/6 π

Where on the unit circle is sin(x) equal to 1?

• At π radians

• At 0 radians

• At π/2 radians

• At 3π/2 radians

What is the angle in radians for sin(x) = 1?

• π

• 3π/2

• π/2

• 2π

How many solutions does the original equation have in the given interval?

• Three

• One

• Two

• Four

Which of the following is not a solution to the original equation?

• π/2

• 7/6 π

• 11/6 π

• 5/6 π