Trigonometric Equations and Solutions

This video tutorial covers solving trigonometric equations using substitution, focusing on half-angle and multiple-angle identities. The instructor demonstrates solving two equations: one involving sine and the other cosine, using substitution to simplify the equations. Reference angles and graphical verification are used to confirm solutions. The video emphasizes understanding the interval of solutions and finding coterminal angles.

What is the first step in solving trigonometric equations using substitution?

• Identify the interval for x

• Directly solve for x without substitution

• Use a calculator to find solutions

• Perform a graphical analysis

When solving the equation sine(u) = sqrt(2)/2, what angle does this remind us of?

• 60 degrees

• 90 degrees

• 45 degrees

• 30 degrees

What are the solutions for x when solving sine(x/2) = sqrt(2) - sine(x/2)?

• x = 90 degrees and 270 degrees

• x = 45 degrees and 135 degrees

• x = 0 degrees and 180 degrees

• x = 180 degrees and 360 degrees

How many points of intersection verify the solutions for the sine equation graphically?

• Three

• Two

• Four

• One

What substitution is made when solving the equation 2cos(3x) - sqrt(3) = 0?

• u = 3x

• u = x/3

• u = 2x

• u = x/2

What is the cosine value that corresponds to a 30-degree angle in a 30-60-90 triangle?

• 1

• sqrt(2)/2

• sqrt(3)/2

• 1/2

How many solutions are found for the cosine equation in terms of x?

• Four

• Seven

• Five

• Six

What is the first solution for x when solving the cosine equation?

• x = 10 degrees

• x = 30 degrees

• x = 60 degrees

• x = 90 degrees

Which quadrant is not considered when finding solutions for cosine(u) = sqrt(3)/2?

• Fourth

• First

• Third

• Second

What is the final solution for x in the cosine equation?

• x = 330 degrees

• x = 360 degrees

• x = 370 degrees

• x = 350 degrees