Solving Cosecant Equations and Angles

The video tutorial explains how to find the four smallest positive radian solutions to the trigonometric equation cosecant 4 theta - 4 = 0. The process involves isolating the trigonometric function, transforming the equation using the sine function, and performing a substitution to solve for U. The solutions are found using a calculator, considering the positive sine values in the first and second quadrants. Additional coterminal solutions are calculated, and the final step involves converting these solutions from U to Theta.

What is the first step in solving the equation cosecant 4 theta - 4 = 0?

• Multiply both sides by 4

• Divide both sides by 4

• Add 4 to both sides

• Subtract 4 from both sides

Why is it easier to solve the equation using the sine function instead of cosecant?

• Cosecant is a complex function

• Sine is a simpler function

• Cosecant is not defined for all angles

• Sine and cosecant are reciprocals

What substitution is made to simplify solving the equation?

• U = theta/4

• U = theta

• U = 2 theta

• U = 4 theta

Why can't sine function values of 1/4 be found using the unit circle?

• The unit circle only includes integer values

• 1/4 is not a standard angle

• The unit circle is only for cosine values

• 1/4 is not a possible sine value

What mode should the calculator be in to solve for U?

• Scientific mode

• Radian mode

• Graphing mode

• Degree mode

What is the first solution for U in radians?

• 3.2527

• 2.2527

• 1.2527

• 0.2527

How is the second solution for U found?

• By dividing the first solution by 2

• By adding 2π to the first solution

• By doubling the first solution

• By subtracting the reference angle from π

What is the process to find the third and fourth solutions for U?

• Multiply the first two solutions by 2

• Add 2π to the first two solutions

• Subtract π from the first two solutions

• Add π to the first two solutions

How do you convert the solutions from U to theta?

• Subtract 4

• Multiply by 4

• Divide by 4

• Add 4

What is the smallest positive radian solution for theta?

• 0.722

• 1.634

• 0.063

• 2.293