solving a trigonometric equation with sine

The video tutorial explains how to solve the trigonometric equation 2 sine squared x = sine x using algebraic methods and the unit circle. It covers simplifying the equation, applying the zero-product property, and finding solutions on the unit circle. The tutorial also discusses how to determine all possible solutions for the equation.

What is the first step in solving the equation 2x^2 = x using algebraic methods?

• Multiply both sides by 2

• Divide both sides by x

• Add x to both sides

• Subtract x from both sides

After factoring the equation 2x^2 - x = 0, what are the possible values of x?

• x = 1 and x = 2

• x = 1/2 and x = 1

• x = 0 and x = 1

• x = 0 and x = 1/2

Where on the unit circle is sine of x equal to 0?

• At angles 0 and pi

• At angles pi/2 and 3pi/2

• At angles pi/4 and 3pi/4

• At angles pi/6 and 5pi/6

At which angles on the unit circle is sine of x equal to 1/2?

• pi/6 and 5pi/6

• pi/3 and 2pi/3

• pi/2 and 3pi/2

• pi/4 and 3pi/4

How can you express the general solution for sine of x = 0?

• x = pi + pi k

• x = 2pi + pi k

• x = pi/6 + 2pi k

• x = pi/4 + pi k

What is the general solution for sine of x = 1/2?

• x = pi/3 + pi k

• x = pi/6 + 2pi k

• x = pi/2 + pi k

• x = pi/4 + 2pi k

Which of the following is a correct expression for the general solution of 5pi/6?

• x = 5pi/6 + 4pi k

• x = 5pi/6 + 3pi k

• x = 5pi/6 + 2pi k

• x = 5pi/6 + pi k