Trigonometric Equations and Functions

The video tutorial explains how to solve a trigonometric equation in quadratic form over the interval from 0 to 2π. The equation is not factorable, so the quadratic formula is applied, with a, b, and c values identified. The solution involves finding cosine values and using inverse cosine to determine theta in radians. The process requires a calculator, ensuring it is in radian mode. The tutorial covers finding angles in different quadrants and calculating reference angles to find all possible solutions. The final solutions are presented in radians, rounded to three decimal places.

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

• 0 to π

• 0 to 4π

• 0 to 2π

• π to 2π

Which formula is used to solve the trigonometric equation in quadratic form?

• Cosine Rule

• Sine Rule

• Quadratic Formula

• Pythagorean Theorem

What are the coefficients a, b, and c in the quadratic equation?

• a = -3, b = 8, c = 4

• a = 3, b = 4, c = -8

• a = 8, b = -4, c = -3

• a = 4, b = -8, c = 3

What is the approximate value of theta when cosine theta equals 0.9114?

• 0.424 radians

• 4.289 radians

• 1.995 radians

• 5.859 radians

In which quadrants is the cosine function positive?

• First and Fourth

• Second and Third

• First and Second

• Third and Fourth

What is the approximate value of theta in the fourth quadrant for cosine theta equals 0.9114?

• 4.289 radians

• 5.859 radians

• 1.995 radians

• 0.424 radians

What is the approximate value of theta when cosine theta equals -0.4114?

• 4.289 radians

• 5.859 radians

• 1.995 radians

• 0.424 radians

In which quadrants is the cosine function negative?

• First and Second

• Second and Third

• First and Fourth

• Third and Fourth

What is the approximate value of theta in the third quadrant for cosine theta equals -0.4114?

• 4.289 radians

• 5.859 radians

• 1.995 radians

• 0.424 radians

How many solutions are there for the trigonometric equation over the interval from 0 to 2π?

• Five

• Four

• Three

• Two