How to determine sine of a half angle using the formula

The video tutorial explains how to solve a trigonometric problem involving Theta and its half-angle. It begins with setting up the problem and introducing the necessary formula for sine of Theta divided by 2. The instructor then discusses the constraints and calculates Theta. The cosine of Theta is evaluated, and the expression is simplified to find the final answer. The tutorial emphasizes understanding patterns and equivalence in mathematical expressions.

What is the formula for sine of Theta divided by 2?

• cosine(Theta) / 2

• 1 - cosine(Theta) / 2

• sqrt(1 - cosine(Theta) / 2)

• sqrt(1 + cosine(Theta) / 2)

If Theta over 2 is π/8, what is the value of Theta?

• π/3

• π/2

• π/4

• π/6

What is the cosine of π/4?

• 0

• 1/2

• 1

• sqrt(2) / 2

How can the expression sqrt(2 - sqrt(2)) / 2 be rewritten?

• As a decimal

• As a negative number

• As a fraction with 1/2 in front

• As a whole number

Why is it important to recognize patterns in solving trigonometric problems?

• To avoid using calculators

• To impress others with knowledge

• To solve problems faster and more efficiently

• To memorize all formulas