Exam Review How to determine the number of solutions for a trigonometric equation

The video tutorial explains how to solve a trigonometric equation involving cosine terms by treating it like a quadratic equation. The instructor demonstrates factoring the equation and applying the zero product property to find solutions. The solutions are analyzed using both the unit circle and graphical approaches, considering constraints between 0 and 2π. The tutorial concludes with identifying three solutions, emphasizing the importance of understanding cosine values and their graphical representation.

What is the first step in solving a trigonometric equation with multiple cosine terms?

• Convert to sine terms

• Use the Pythagorean identity

• Treat the equation like a quadratic and factor it

• Isolate each cosine term separately

What property is applied after factoring a trigonometric equation to find solutions?

• Subtraction property

• Addition property

• Zero product property

• Pythagorean property

On the unit circle, at what angle is the cosine value equal to -1?

• π

• π/2

• 0

• 2π

Why is the cosine value of 2/3 considered valid in the context of the problem?

• It is greater than 1

• It is equal to 1

• It is a common trigonometric value

• It is less than 1 and within the range of cosine values

How many times does the cosine graph intersect the value 2/3 within one period?

• Four times

• Three times

• Twice

• Once