Solving Trig Equations with Period Changes

The video tutorial explains how to solve the equation cosine of 2 theta equals zero within the interval from 0 to 2pi. It discusses the impact of the 2 theta term on the period of the cosine function, requiring consideration of additional cycles. The tutorial demonstrates solving for theta using inverse cosine and integer K to account for multiple rotations. It identifies valid solutions within the specified interval, ensuring they are less than 2pi.

What is the result of cosine of two theta equals zero within the interval 0 to 2pi?

• Theta equals pi/4, 3pi/4, 5pi/4, 7pi/4

• Theta equals pi/2, pi, 3pi/2, 2pi

• Theta equals 0, pi/4, pi/2, pi

• Theta equals 0, pi/2, pi, 3pi/2

What does the factor of two in the angle theta change about the cosine function?

• It quadruples the period of the function.

• It halves the period of the function.

• It does not affect the period of the function.

• It doubles the period of the function.

What is the significance of adding 2pi times K in the solutions?

• It eliminates negative solutions.

• It limits the solutions to the first quadrant.

• It reduces the number of possible solutions.

• It accounts for all possible rotations around the unit circle.

How do you derive the general solution for theta from the equation 2 theta equals pi/2 and 3pi/2?

• Divide both sides by 2 and subtract pi times K.

• Multiply both sides by 1/2 and add pi times K.

• Multiply both sides by 2 and add pi times K.

• Divide both sides by 2 and add 2pi times K.

Which of the following is a correct interpretation of the equation 2 theta equals pi/2?

• Theta equals pi/4.

• Theta equals pi/2.

• Theta equals pi.

• Theta equals 2pi.

What is the effect of multiplying the equation 2 theta equals pi/2 by 1/2?

• Theta equals pi/4.

• Theta equals pi/2.

• Theta equals 2pi.

• Theta equals pi.

What values of K provide valid solutions within the interval 0 to 2pi?

• K = 0, 1, 2, 3

• K = 0, 1

• K = 0, 1, 2

• K = -1, 0, 1

What happens if K equals 2 in the derived formulas for theta?

• It results in theta values larger than 2pi, which are invalid.

• It does not affect the solutions.

• It provides additional valid solutions.

• It results in negative theta values, which are invalid.

Which of the following is not a solution for the equation cosine of two theta equals zero?

• Theta equals pi.

• Theta equals 3pi/4.

• Theta equals pi/4.

• Theta equals 2pi.

How many valid solutions exist for the equation within the interval 0 to 2pi?

• Two solutions

• Three solutions

• Four solutions

• Five solutions