Trigonometric Functions and Identities

This video tutorial covers solving trigonometric equations using substitution. It begins with an introduction to the method and then provides two examples: one involving a cosine equation and the other a sine equation. The tutorial demonstrates how to use trigonometric identities and the unit circle to find solutions, and it also discusses checking solutions graphically.

What is the primary focus of the video tutorial in part two?

• Graphing linear functions

• Calculating derivatives

• Using substitution in trigonometric equations

• Solving algebraic equations

Which identity is used to substitute cosine 2 Theta in the equation?

• cosine 2 Theta = 1 - 2 sine^2 Theta

• cosine 2 Theta = 2 sine Theta

• cosine 2 Theta = sine^2 Theta - cosine^2 Theta

• cosine 2 Theta = 2 cosine^2 Theta - 1

What is the first step in solving the equation after substitution?

• Differentiating the equation

• Factoring the equation

• Using the quadratic formula

• Graphing the equation

Which angles are solutions for cosine Theta = -1/2 on the unit circle?

• 2Pi/3 and 4Pi/3

• Pi/2 and 3Pi/2

• 0 and Pi

• Pi/3 and 5Pi/3

How can the solutions be verified graphically?

• By plotting sine Theta

• By plotting cosine 2 Theta - cosine Theta

• By plotting sine 2 Theta

• By plotting tangent Theta

What substitution is used for sine 2 Theta in the second example?

• sine 2 Theta = cosine^2 Theta - sine^2 Theta

• sine 2 Theta = 2 sine Theta cosine Theta

• sine 2 Theta = 1 - 2 cosine^2 Theta

• sine 2 Theta = 2 cosine^2 Theta - 1

What common factor is factored out in the second example?

• secant Theta

• tangent Theta

• sine Theta

• cosine Theta

Which angles are solutions for sine Theta = 0 on the unit circle?

• Pi/2 and 3Pi/2

• 2Pi/3 and 4Pi/3

• Pi/3 and 5Pi/3

• 0 and Pi

What is the x-coordinate for cosine Theta = 1/2 on the unit circle?

• 1/2

• 1

• 0

• -1/2

How many points of intersection are there in the graphical verification of the second example?

• Five

• Four

• Three

• Two