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

The video tutorial explains how to find the cosine of Theta over 2 for a triangle using the formula sqrt(1 + cos(Theta)/2). It covers the importance of understanding when to use positive or negative square roots based on the angle's position. The tutorial demonstrates using the Pythagorean theorem to find the hypotenuse and evaluates the cosine of Theta. It also includes steps to simplify fractions and rationalize the denominator to reach the final answer.

What is the formula for finding the cosine of Theta over 2?

• sqrt(1 - sine of Theta) / 2

• sqrt(1 - cosine of Theta) / 2

• sqrt(1 + cosine of Theta) / 2

• sqrt(1 + sine of Theta) / 2

Why is it important to know whether to use the positive or negative square root in the formula?

• It affects the angle's degree measure.

• It determines the triangle's type.

• It depends on the angle's position.

• It changes the triangle's area.

Which Pythagorean triple is used to find the hypotenuse in this problem?

• 7, 24, 25

• 3, 4, 5

• 5, 12, 13

• 8, 15, 17

What operation is performed to simplify the fraction 32/34?

• Subtract 2

• Add 2

• Divide by 2

• Multiply by 2

What is the final simplified form of the expression for cosine of Theta over 2?

• 4 sqrt(17) / 17

• 2 sqrt(17) / 17

• sqrt(17) / 4

• 17 / 4 sqrt(17)