Trigonometric Equations and Angles

The video tutorial guides viewers through solving a trigonometric equation in quadratic form. It begins by identifying the need to use the quadratic formula, substituting values, and simplifying to find cosine theta. The tutorial explains why one solution is invalid due to the cosine function's range and demonstrates how to find valid solutions using inverse cosine. It further explores finding reference angles in different quadrants to determine all possible solutions within the interval from zero to two pi. The tutorial concludes with the final solutions, rounded to three decimal places.

What is the interval within which the solutions for the trigonometric equation are to be found?

• 0 to 4π

• π to 2π

• 0 to 2π

• 0 to π

What are the values of a, b, and c in the quadratic formula for this problem?

• a = 2, b = -4, c = -3

• a = 3, b = -6, c = -2

• a = 4, b = -5, c = -1

• a = 6, b = -8, c = -6

What is the approximate value of cosine theta when using the positive square root in the quadratic formula?

• -0.5352

• 1.5362

• 1.8685

• 0.5352

Why is the solution with cosine theta approximately 1.8685 not valid?

• The value is undefined in radians

• Cosine values cannot exceed 1

• The value is not in the given interval

• Cosine values cannot be negative

What is the approximate value of theta when cosine theta is -0.5352?

• 4.136 radians

• 2.136 radians

• 1.136 radians

• 3.136 radians

In which quadrants is the cosine function negative?

• Second and third

• First and second

• First and fourth

• Third and fourth

What is the reference angle for the angle 2.136 radians in the second quadrant?

• 0.136 radians

• 1.006 radians

• 3.006 radians

• 2.006 radians

How do you find the angle in the third quadrant with the same cosine value as the reference angle?

• Subtract the reference angle from π

• Add the reference angle to 2π

• Subtract the reference angle from 2π

• Add the reference angle to π

What is the approximate value of the angle in the third quadrant?

• 5.148 radians

• 4.148 radians

• 6.148 radians

• 3.148 radians

What are the two solutions for theta in the given interval?

• 1.136 and 3.148 radians

• 4.136 and 6.148 radians

• 3.136 and 5.148 radians

• 2.136 and 4.148 radians