How to determine the half angle of tangent when given a triangle

The video tutorial covers the evaluation of the cosecant function, starting with its relation to the unit circle and the need to construct a triangle when the point is not on the circle. It explains how to determine the quadrant of an angle based on given constraints and introduces the cosecant function as the ratio of the hypotenuse to the opposite side. The tutorial also covers the tangent of a half angle, providing formulas and calculations, and concludes with final calculations and a summary of the lesson.

In which quadrant does the angle lie if it is between π and 3π/2?

• Third quadrant

• Fourth quadrant

• First quadrant

• Second quadrant

What is the ratio for the cosecant function?

• Opposite over hypotenuse

• Hypotenuse over adjacent

• Adjacent over hypotenuse

• Hypotenuse over opposite

Which of the following is a Pythagorean triple?

• All of the above

• (5, 12, 13)

• (3, 4, 5)

• (8, 15, 17)

What is the formula for the tangent of a half angle?

• 2 tangent of U / 1 + tangent squared of U

• 1 - cosine of U divided by sine

• 2 tangent of U / 1 - tangent squared of U

• 1 + cosine of U divided by sine

What is the result of the tangent of the half angle calculation in the third section?

• -5

• 5

• 3

• -3