Using the half angle of sine to evaluate an angle

The video tutorial explains how to evaluate the sine of 3π/8, which is not on the unit circle. Initially, the sum and difference formulas are considered, but the half-angle formula is introduced as a more efficient method. The tutorial demonstrates how to apply the half-angle formula, simplify the expression, and arrive at the final result. Key concepts include understanding the unit circle, using trigonometric identities, and applying algebraic simplification techniques.

Why is the sine of 3π/8 not directly available on the unit circle?

• The unit circle does not include eighths.

• The unit circle only includes angles in radians.

• The unit circle is only divided into quarters.

• The unit circle only includes angles in degrees.

What is the main advantage of using the half-angle formula over the sum and difference formulas?

• It can be used for any angle.

• It is less time-consuming.

• It is more accurate.

• It requires less memorization.

What is the half-angle formula for sine?

• sin(θ/2) = ± sqrt(1 - sin(θ))/2

• sin(θ/2) = ± sqrt(1 - cos(θ))/2

• sin(θ/2) = ± sqrt(1 + cos(θ))/2

• sin(θ/2) = ± sqrt(1 + sin(θ))/2

In which quadrant does the angle 3π/8 lie, and what is the sign of sine in that quadrant?

• Fourth quadrant, negative

• Third quadrant, negative

• Second quadrant, positive

• First quadrant, positive

What is the cosine of 3π/4?

• 0

• -1

• sqrt(2)/2

• -sqrt(2)/2

What is the result of simplifying the expression 1 - (-sqrt(2)/2) divided by 2?

• 1/2 + sqrt(2)/4

• 1/2 - sqrt(2)/4

• 1/2 - sqrt(2)/2

• 1/2 + sqrt(2)/2

What is the final simplified form of the expression 2 + sqrt(2) all over 2?

• 2 + sqrt(2)/2

• sqrt(2)

• 1 + sqrt(2)/2

• 1 + sqrt(2)