Understanding Cosine and Half-Angle Identities

The video tutorial explains how to find the cosine of u divided by two using the half-angle identity. It starts by introducing the problem and setting up a reference triangle for angle u in quadrant four. The tutorial then uses the Pythagorean theorem to calculate the x-coordinate of the triangle. Finally, it determines the cosine of u divided by two, considering the sign based on the quadrant, and concludes with the final result.

What is the half-angle identity used to find cosine of u/2?

• cos(u/2) = ±√(1 - cos(u))/2

• cos(u/2) = ±√(1 - sin(u))/2

• cos(u/2) = ±√(1 + sin(u))/2

• cos(u/2) = ±√(1 + cos(u))/2

In which quadrant is angle u located?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What is the value of cosecant u given in the problem?

• 2.381

• -2.381

• 1.381

• -1.381

What is the relationship between r, y, and cosecant u?

• y/r = cosecant u

• x/r = cosecant u

• r/x = cosecant u

• r/y = cosecant u

What is the approximate value of x calculated using the Pythagorean theorem?

• 0.160824

• 3.160824

• 1.160824

• 2.160824

In which quadrant does angle u/2 lie?

• Quadrant III

• Quadrant II

• Quadrant I

• Quadrant IV

Why is the cosine of u/2 negative?

• Because u/2 is in Quadrant III

• Because u/2 is in Quadrant II

• Because u/2 is in Quadrant IV

• Because u/2 is in Quadrant I

What is the formula for cosine u in terms of x and r?

• cos(u) = x/r

• cos(u) = r/x

• cos(u) = y/r

• cos(u) = r/y

What is the final approximate value of cosine of u/2?

• 0.79

• -0.79

• 0.97

• -0.97

What is the significance of the sign in the half-angle identity?

• It determines the length of the opposite side

• It determines the length of the hypotenuse

• It determines the quadrant of the original angle

• It determines the quadrant of the half-angle