Half Angle Identities Quiz

What is the formula for the sine of half an angle derived from the double angle identity for cosine?

• sin(a/2) = ±√((1 + cos(a))/2)

• sin(a/2) = ±√((1 - cos(a))/2)

• sin(a/2) = ±√((1 - sin(a))/2)

• sin(a/2) = ±√((1 + sin(a))/2)

How do you determine the sign of the sine half angle identity?

• Based on the quadrant of the original angle

• Based on the angle's sine value

• Based on the angle's magnitude

• Based on the angle's cosine value

What is the formula for the cosine of half an angle?

• cos(a/2) = ±√((1 - sin(a))/2)

• cos(a/2) = ±√((1 + sin(a))/2)

• cos(a/2) = ±√((1 + cos(a))/2)

• cos(a/2) = ±√((1 - cos(a))/2)

Why is the sign of the cosine half angle identity important?

• It affects the angle's sine value

• It determines the angle's magnitude

• It is irrelevant to the calculation

• It depends on the quadrant of the angle

Which of the following is NOT a form of the tangent half angle identity?

• tan(a/2) = ±√((1 + sin(a))/(1 - sin(a)))

• tan(a/2) = ±√((1 - cos(a))/(1 + cos(a)))

• tan(a/2) = sin(a)/(1 + cos(a))

• tan(a/2) = (1 - cos(a))/sin(a)

In the example of finding the sine of 9π/8, which quadrant is 9π/8 located in?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What is the exact value of sin(9π/8) using the half angle identity?

• -√2/4

• √2/4

• √2/2

• -√2/2

In the example of finding the cosine of x/2, what is the given range for x?

• 0 to π/2

• π/2 to π

• π to 3π/2

• 3π/2 to 2π

What is the cosine of x if sin(x) = 4/5 and x is in Quadrant IV?

• -4/5

• 4/5

• -3/5

• 3/5

What is the exact value of cos(x/2) if x is in Quadrant IV and sin(x) = 4/5?

• √5/5

• -√5/5

• -2√5/5

• 2√5/5