Solving Trigonometric Equations and Identities

This video is the third in a series on solving trigonometric equations. It covers solving equations using identities, handling non-factorable equations, and solving by squaring both sides. The video provides examples and checks solutions using a graphing calculator. It emphasizes the importance of verifying solutions to avoid extraneous results.

What is the main focus of this video in the series?

• Introduction to basic trigonometric functions

• Solving trigonometric equations with identities, non-factorable equations, and squaring both sides

• Solving trigonometric equations using graphs

• Graphing trigonometric functions

Which identity is used to substitute for sine squared x in the first problem?

• Sine squared x + cosine squared x = 1

• Sine x = cosine x

• Tangent squared x + 1 = secant squared x

• Cosine squared x - sine squared x = 1

What is the reference angle used when solving for cosine x = ±√3/2?

• 60 degrees

• 45 degrees

• 90 degrees

• 30 degrees

Which identity is used to solve the equation by squaring both sides?

• Sine squared x + cosine squared x = 1

• Tangent squared theta + 1 = secant squared theta

• Cosine squared x - sine squared x = 1

• Sine x = cosine x

What is the tangent function value for the angles found in the second problem?

• -√3

• √3

• -1/√3

• 1/√3

Why is it important to check solutions when squaring both sides of an equation?

• To confirm the equation is factorable

• To check for symmetry

• To ensure no extraneous solutions are included

• To verify the graph is correct

What is the correct solution for the tangent equation after checking for extraneous solutions?

• 150 degrees

• 90 degrees

• 330 degrees

• 210 degrees

What method is used to solve the non-factorable trigonometric equation?

• Completing the square

• Quadratic formula

• Substitution

• Graphing

What is the approximate degree measure of the angle found using the quadratic formula?

• 107.6 degrees

• 180 degrees

• 90 degrees

• 72.4 degrees

In which quadrants is the cosine function negative?

• First and second

• Second and third

• Third and fourth

• First and fourth