Trigonometric Functions and Identities

The video tutorial explains how to find the cosine of u divided by two using the half-angle identity. Given that cotangent u is 3.25 and angle u is in quadrant three, the tutorial guides through sketching a reference triangle, calculating the hypotenuse using the Pythagorean theorem, and determining the cosine of u/2. The process involves understanding the signs of trigonometric functions in different quadrants and using a calculator for precise values.

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

• 2.75

• 3.25

• 3.50

• 4.00

In which quadrant is angle u located?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

What is the half-angle identity for cosine?

• cos(a/2) = ±√(1 + cos(a))/2

• cos(a/2) = ±√(1 - cos(a))/2

• cos(a/2) = ±√(1 + sin(a))/2

• cos(a/2) = ±√(1 - sin(a))/2

What is the relationship between cotangent and the sides of a triangle?

• Hypotenuse/Adjacent

• Hypotenuse/Opposite

• Opposite/Adjacent

• Adjacent/Opposite

What are the signs of x and y in quadrant three?

• Both x and y are positive

• x is positive, y is negative

• x is negative, y is positive

• Both x and y are negative

What formula is used to find the hypotenuse in a right triangle?

• a^2 - b^2 = c

• a^2 + b^2 = c

• a^2 - b^2 = c^2

• a^2 + b^2 = c^2

What is the approximate value of the hypotenuse calculated in the problem?

• 3.500

• 3.250

• 3.400

• 3.600

In which quadrant is angle u/2 located?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

What is the sign of cosine in quadrant two?

• Undefined

• Zero

• Negative

• Positive

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

• 0.2487

• 0.1487

• -0.1487

• -0.2487