How to evaluate the half angle of cosine when given a triangle

The video tutorial explains the half angle formula for cosine, focusing on when to use the positive or negative sign based on the angle's quadrant. It demonstrates finding the hypotenuse using the Pythagorean theorem and calculating cosine by simplifying fractions and rationalizing the denominator. The tutorial provides a step-by-step approach to solving similar problems.

What determines whether the result of the half angle formula is positive or negative?

• The length of the hypotenuse

• The type of triangle used

• The size of the angle

• The quadrant in which the angle lies

Which theorem is used to find the hypotenuse when calculating cosine?

• Tangent theorem

• Cosine rule

• Sine rule

• Pythagorean theorem

What is the cosine of an angle defined as in a right triangle?

• Hypotenuse over adjacent

• Adjacent over hypotenuse

• Opposite over hypotenuse

• Adjacent over opposite

What is the first step in simplifying the cosine expression?

• Adding the fractions

• Multiplying by the reciprocal

• Combining like terms

• Rationalizing the denominator

What is the final simplified form of the cosine expression in this problem?

• 4 / sqrt 17

• 32 / 34

• 4 sqrt 17 / 17

• 16 / 17