Trigonometric Equations and Solutions

The video tutorial explains how to solve a trigonometric equation within a specified interval, both in degrees and radians. It begins by clarifying the closed and open nature of the interval, then demonstrates how to factor the equation by setting it to zero and factoring out sine x. The solutions are found by solving for sine x and cosine x using the unit circle, identifying the angles where these values occur. The tutorial concludes by summarizing the solutions in degrees, as the interval was given in degrees.

What does it mean when an interval is closed on zero degrees?

• It includes zero degrees.

• It excludes zero degrees.

• It includes 360 degrees.

• It excludes 360 degrees.

How do you start solving a trigonometric equation with a common factor?

• By multiplying both sides by zero.

• By factoring out the common factor.

• By dividing both sides by the common factor.

• By adding a constant to both sides.

What is the first step in solving the equation 2 cosine x sine x - sine x = 0?

• Factor out sine x.

• Divide both sides by sine x.

• Add sine x to both sides.

• Multiply both sides by cosine x.

When sine x equals zero, what are the possible angles in degrees?

• 60 degrees and 300 degrees

• 0 degrees and 180 degrees

• 90 degrees and 270 degrees

• 45 degrees and 225 degrees

On the unit circle, where is cosine x equal to one-half?

• At 45 degrees and 225 degrees

• At 60 degrees and 300 degrees

• At 0 degrees and 180 degrees

• At 90 degrees and 270 degrees

Why is 360 degrees not included in the solution set?

• Because the interval is open on 360 degrees.

• Because it is equivalent to zero degrees.

• Because 360 degrees is not a valid angle.

• Because the equation does not allow it.

What is the solution for cosine x equals one-half in radians?

• Pi over 2 and 3 pi over 2

• Pi over 3 and 5 pi over 3

• Pi and 2 pi

• Pi over 4 and 3 pi over 4

Which angles are solutions for the equation in degrees?

• 45 degrees, 135 degrees, 225 degrees, 315 degrees

• 30 degrees, 150 degrees, 210 degrees, 330 degrees

• 0 degrees, 180 degrees, 60 degrees, 300 degrees

• 0 degrees, 90 degrees, 180 degrees, 270 degrees

What is the significance of the interval in determining solutions?

• It affects the unit circle's size.

• It changes the trigonometric functions used.

• It limits the range of possible solutions.

• It determines the method of solving.

If the interval was given in radians, what would be the solutions?

• pi/6 radians, 5pi/6 radians, 7pi/6 radians, 11pi/6 radians

• pi/4 radians, 3pi/4 radians, 5pi/4 radians, 7pi/4 radians

• 0 radians, pi/2 radians, pi radians, 3pi/2 radians

• 0 radians, pi radians, pi/3 radians, 5pi/3 radians