Learn how to evaluate the half angle for sine in radians

The video tutorial explains how to find the sine of an angle not on the unit circle using the sum and difference formula. It starts by discussing the unit circle and the angle 5π/8, then introduces the sum and difference formula. The tutorial guides viewers through determining the value of U in the formula and simplifying the trigonometric expression. The final section covers the calculation steps and concludes with the solution.

What is the equivalent of π in terms of eighths on the unit circle?

• 4π/8

• 2π/8

• 8π/8

• 5π/8

In the sum and difference formula for sine, what does U represent when calculating sine of 5π/8?

• 5π/8

• π/2

• 5π/4

• π/4

Why is the plus or minus sign important in the sine half-angle formula?

• It shows whether sine is positive or negative based on the quadrant.

• It is used to calculate the cosine of the angle.

• It indicates whether the angle is acute or obtuse.

• It determines the angle's position on the unit circle.

In which quadrant is the angle 5π/8 located, and what is the sign of sine in that quadrant?

• First quadrant, positive

• Fourth quadrant, negative

• Second quadrant, positive

• Third quadrant, negative

What is the reference angle for 5π/4, and in which quadrant does it lie?

• π/4, first quadrant

• π/4, second quadrant

• π/4, third quadrant

• π/4, fourth quadrant

How can the expression sqrt(a/b) be rewritten?

• sqrt(a) + sqrt(b)

• a / sqrt(b)

• sqrt(a) / sqrt(b)

• sqrt(a) * sqrt(b)

What is the simplified form of the expression 2 + sqrt(2) / 2?

• 1/2 * sqrt(2) + 2

• 1/2 * (2 + sqrt(2))

• 2 * sqrt(2) / 2

• sqrt(2) + 1/2