Evaluate for theta between 0 and 2pi

The video tutorial explains how to evaluate Theta when the cosecant of Theta equals 2√3/3. It begins by discussing the relationship between cosecant and sine, emphasizing that cosecant is the reciprocal of sine. The instructor demonstrates how to find the reciprocal of coordinate points and rationalize the denominator to match the given cosecant value. The tutorial then identifies angles where sine equals √3/2, which corresponds to the given cosecant value. Finally, it explains the reflection over the Y-axis to find additional angles, concluding with the angles π/3 and 2π/3 as solutions.

What is the relationship between cosecant and sine?

• Cosecant is the square of sine.

• Cosecant is the inverse of sine.

• Cosecant is the reciprocal of sine.

• Cosecant is the derivative of sine.

What is the first step in evaluating theta when given a cosecant value?

• Use the Pythagorean theorem.

• Find the reciprocal of the sine value.

• Convert the angle to degrees.

• Find the tangent of the angle.

What is the sine of theta if the cosecant of theta is 2√3/3?

• 1/2

• √3/2

• 2/√3

• 1/√3

Which angle corresponds to a sine value of √3/2 on the unit circle?

• π/4

• π/2

• π/6

• π/3

What is the second angle where the sine of theta equals √3/2?

• 3π/4

• 2π/3

• 5π/6

• π/4