Trigonometric Equations and Solutions

The video tutorial explains how to solve a trigonometric equation on the interval from 0 to 2π. It begins by factoring the equation and finding solutions for sine theta using the unit circle. The tutorial then addresses solving the cosine equation using a calculator, identifying solutions in the second and third quadrants. Reference angles are calculated to find additional solutions. The video concludes by summarizing the four solutions found within the given interval.

What is the first step in solving the trigonometric equation by factoring?

• Divide both sides by sine theta

• Multiply both sides by cosine theta

• Subtract 8 sine theta from both sides

• Add 8 sine theta to both sides

What are the solutions for sine theta equals zero on the unit circle?

• 0 and 2π

• 0 and π

• π/4 and 3π/4

• π/2 and 3π/2

Why can't we find the cosine theta equals -4/5 value on the unit circle?

• Because it is less than -1

• Because it is a positive value

• Because it is greater than 1

• Because it is not a standard angle

In which quadrants can the solution for cosine theta equals -4/5 be found?

• First and fourth

• Third and fourth

• First and second

• Second and third

What is the approximate angle in radians for cosine theta equals -4/5 in the second quadrant?

• 1.047

• 2.498

• 3.142

• 0.785

What is the reference angle for the solution in the third quadrant?

• 1.570 radians

• 0.644 radians

• 1.047 radians

• 0.785 radians

How do you find the second solution in the third quadrant?

• Divide the reference angle by 2

• Multiply the reference angle by 2

• Subtract the reference angle from π

• Add the reference angle to π

What is the approximate value of the second solution in the third quadrant?

• 2.498 radians

• 3.786 radians

• 1.047 radians

• 0.644 radians

How many total solutions are there for the given trigonometric equation on the interval?

• Three

• Two

• Five

• Four

Which of the following intervals is closed on 0 and open on 2π?

• [0, 2π)

• (0, 2π)

• (0, 2π]

• [0, 2π]