Solving Trigonometric Equations Using Substitution

This video tutorial covers solving trigonometric equations using substitution. It begins with an introduction to the method and proceeds to solve two examples. The first example involves solving equations with half-angle substitution, while the second example deals with multiple angles. The tutorial emphasizes using the unit circle and reference triangles to find solutions and verify them graphically. The video concludes with a promise of more examples in a subsequent part.

What is the primary focus of this lesson on solving trigonometric equations?

• Solving equations using differentiation

• Solving equations using substitution

• Solving equations using integration

• Solving equations using elimination

In the first example, what substitution is made for x/2?

• t = x/5

• w = x/4

• u = x/2

• v = x/3

Which angles in the unit circle correspond to a sine value of √2/2?

• 30° and 150°

• 90° and 180°

• 60° and 120°

• 45° and 135°

What is the value of X when U equals 45° in the first example?

• 360°

• 270°

• 90°

• 180°

In the second example, what substitution is made for 3x?

• v = 2x

• u = 3x

• w = 4x

• t = 5x

Which angles in the unit circle correspond to a cosine value of √3/2?

• 30° and 330°

• 90° and 270°

• 45° and 315°

• 60° and 300°

What is the first solution for X when U equals 30° in the second example?

• 10°

• 40°

• 30°

• 20°

How many solutions for X are found in the second example?

• Two

• Eight

• Four

• Six

What is the next coterminal angle to 30° that is used to find another solution for X?

• 450°

• 390°

• 420°

• 360°

What method is used to verify the solutions graphically?

• Plotting the cosine function

• Plotting both sides of the equation

• Plotting the sine function

• Plotting the tangent function