Learn how to evaluate using the half angle formula of sine

The video tutorial explains the half angle formula for sine and demonstrates how to find the sine of 3π/8 using this formula. It covers solving for U, finding the cosine of 3π/4 using the unit circle, and simplifying the resulting expression. The tutorial emphasizes understanding each step and the importance of the unit circle in trigonometry.

What is the first step in applying the half-angle formula to find the sine of 3π/8?

• Directly calculate the sine of 3π/8.

• Set the half-angle equal to 3π/8.

• Find the cosine of 3π/8.

• Use the double angle formula.

Why do we need to solve for U in the half-angle formula?

• To find the sine of U.

• To find the secant of U.

• To find the cosine of U.

• To find the tangent of U.

What is the cosine of 3π/4 according to the unit circle?

• sqrt 2 / 2

• -sqrt 2 / 2

• 0

• 1

In which quadrant is the angle 3π/4 located?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

Why do we only consider the positive value of the sine in the second quadrant?

• Because tangent is positive in the second quadrant.

• Because sine is positive in the second quadrant.

• Because cosine is negative in the second quadrant.

• Because sine is always positive.

What is the purpose of multiplying by 2/2 in the simplification process?

• To change the value of the expression.

• To eliminate the fraction in the numerator.

• To find the square root of the expression.

• To convert the expression to a decimal.

What is the final simplified form of the expression?

• sqrt 2 + sqrt 2 / 2

• 1/2 * sqrt 2 + sqrt 2 / 2

• sqrt 2 + sqrt 2

• 1/2 * sqrt 2 + sqrt 2