Solving trigonometric equations

The video tutorial explains how to solve the trigonometric equation 2sin²(X) + 3sin(X) + 1 = 0. It begins by discussing the need to factor the equation due to its quadratic form. The instructor demonstrates factoring the equation and applying the zero product property to find solutions. The unit circle is used to identify specific angles where the sine function equals -1 or -1/2. Finally, the tutorial covers finding all possible solutions by considering coterminal angles, emphasizing the periodic nature of the sine function.

What is the first step in solving the equation 2sin²(X) + 3sin(X) + 1 = 0?

• Factor the equation

• Use the quadratic formula

• Graph the function

• Isolate the variable X

After factoring the equation, what property is used to solve for sine of X?

• Zero Product Property

• Associative Property

• Distributive Property

• Commutative Property

Which tool is used to find the specific angles where sine of X equals -1 or -1/2?

• Trigonometric Identities

• Pythagorean Theorem

• Unit Circle

• Graphing Calculator

What is the angle in radians where sine of X equals -1?

• 2π

• 3π/2

• π

• π/2

How do you find all possible solutions for the equation considering the periodic nature of sine?

• Subtract multiples of 2π

• Subtract multiples of π

• Add multiples of 2π

• Add multiples of π