Master Evaluating the half angle for sine, cosine, and tangent given an equation and constraint

The video tutorial explains how to evaluate expressions using half angle formulas. It begins with setting up a triangle in the third quadrant based on given constraints and then uses the Pythagorean theorem to find the hypotenuse and sides. The tutorial covers evaluating sine, cosine, and tangent of the half angle using respective formulas, emphasizing the importance of sign determination based on quadrants. The process involves simplifying fractions and rationalizing denominators, with a focus on understanding the mathematical principles behind each step.

What is the main goal when using half angle formulas in this context?

• To convert angles from radians to degrees

• To determine the half angle values for sine, cosine, and tangent

• To solve for unknown sides of a triangle

• To find the full angle values

In which quadrant is the triangle constructed based on the given constraints?

• Third quadrant

• Second quadrant

• First quadrant

• Fourth quadrant

What is the significance of the negative signs for the sides of the triangle in the third quadrant?

• They suggest the triangle is in the fourth quadrant

• They confirm the triangle is in the third quadrant

• They show the triangle is in the second quadrant

• They indicate the triangle is in the first quadrant

Which method is used to calculate the hypotenuse in this scenario?

• Law of Sines

• Law of Cosines

• Trigonometric identities

• Pythagorean theorem

What is the half angle formula for sine?

• ± sqrt(1 + sin(θ) / 2)

• ± sqrt(1 - cos(θ) / 2)

• ± sqrt(1 + cos(θ) / 2)

• ± sqrt(1 - sin(θ) / 2)

Why is it important to consider the sign of the square root in the half angle formula?

• It alters the angle to degrees

• It changes the angle to radians

• It determines the length of the hypotenuse

• It affects the quadrant of the angle

What is the result of evaluating cosine using the half angle formula in this context?

• Undefined

• Zero

• Negative value

• Positive value

Which formula is preferred for evaluating tangent in this lesson?

• 1 - cos(α) / sin(α)

• sin(α) / 1 + cos(α)

• cos(α) / sin(α)

• ± sqrt(1 - cos(θ) / 1 + cos(θ))

What is the final result of evaluating tangent using the half angle formula?

• Positive 2

• Negative 2

• Negative 4

• Positive 4

What is the main advantage of using the tangent half angle formula mentioned?

• It is applicable to all quadrants

• It requires fewer calculations

• It avoids using square roots

• It simplifies to a single value