Master Evaluating using the half angle formulas given an equation and constraint

The video tutorial explains how to evaluate expressions using half angle formulas, focusing on sine, cosine, and tangent. It begins with an introduction to the Cartesian coordinate system and the positioning of angles. The tutorial then guides viewers through creating and analyzing triangles, applying the Pythagorean theorem, and using half angle formulas to evaluate trigonometric functions. The video emphasizes understanding the constraints and properties of angles in different quadrants.

What is the primary focus when evaluating expressions using half angle formulas?

• Using only the sine function

• Memorizing all trigonometric identities

• Understanding the given equation and constraints

• Finding the exact value of the angle

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

• Third quadrant

• First quadrant

• Second quadrant

• Fourth quadrant

What is the reciprocal of the cosine function?

• Sine

• Cosecant

• Tangent

• Secant

Which theorem is used to find the missing side of a right triangle?

• Pythagorean theorem

• Sine rule

• Cosine rule

• Tangent theorem

How do you determine if the sine of the half angle is positive or negative?

• By using the cosine value

• By checking the original angle's quadrant

• By the length of the opposite side

• By the length of the hypotenuse

What is the formula used to calculate the cosine of the half angle?

• 1 - sine of alpha divided by two

• 1 + cosine of alpha divided by two

• 1 - tangent of alpha divided by two

• 1 + secant of alpha divided by two

Why is it important to rationalize the denominator in trigonometric expressions?

• To ensure the expression is in standard form

• To make calculations easier

• To avoid complex numbers

• To simplify the expression

Which formula is preferred for calculating the tangent of the half angle?

• 1 - cosine of alpha divided by sine of alpha

• Cosine of alpha divided by 1 - sine of alpha

• 1 + cosine of alpha divided by sine of alpha

• Sine of alpha divided by 1 + cosine of alpha

What is the result of rationalizing the expression 2/sqrt(2)?

• sqrt(3)

• sqrt(2)

• 2

• 1

What is the final simplified form of the tangent of the half angle in this problem?

• 2/sqrt(3)

• 1/sqrt(3)

• sqrt(2)

• sqrt(3)/3