Trigonometric Functions and Identities

The video tutorial explains how to find the exact values of trigonometric functions using half-angle identities. Starting with a given sine value in the third quadrant, the tutorial guides through setting up a reference triangle, calculating cosine, and using half-angle identities to find sine, cosine, and tangent of half the angle. The process involves using the Pythagorean theorem and simplifying complex fractions, with a focus on understanding quadrant-specific sign changes.

In which quadrant is angle u located if sine u is negative three-eighths?

• Second quadrant

• First quadrant

• Third quadrant

• Fourth quadrant

What is the value of y in the reference triangle if sine u is negative three-eighths?

• -3

• 8

• 3

• -8

Using the Pythagorean theorem, what is the value of x in the reference triangle?

• Square root of 64

• -Square root of 64

• Square root of 55

• -Square root of 55

What is the cosine of angle u in the reference triangle?

• 3 divided by 8

• -3 divided by 8

• -Square root of 55 divided by 8

• Square root of 55 divided by 8

In which quadrant is angle u/2 located?

• First quadrant

• Second quadrant

• Fourth quadrant

• Third quadrant

What is the sine of u/2 using the half-angle identity?

• Square root of (8 + square root of 55) divided by 4

• Negative square root of (8 + square root of 55) divided by 4

• Square root of (8 - square root of 55) divided by 4

• Negative square root of (8 - square root of 55) divided by 4

What is the cosine of u/2 using the half-angle identity?

• Square root of (8 + square root of 55) divided by 4

• Square root of (8 - square root of 55) divided by 4

• Negative square root of (8 + square root of 55) divided by 4

• Negative square root of (8 - square root of 55) divided by 4

Which formula can be used to find tangent of u/2?

• Cosine of u/2 divided by sine of u/2

• Cosine of u divided by sine of u

• Sine of u/2 divided by cosine of u/2

• Sine of u divided by cosine of u

What is the tangent of u/2 using the given values?

• Negative 3 divided by (8 + square root of 55)

• 3 divided by (8 - square root of 55)

• Negative 3 divided by (8 - square root of 55)

• 3 divided by (8 + square root of 55)

What is the final step in simplifying the expression for tangent of u/2?

• Divide numerator and denominator by 8

• Subtract 8 from both numerator and denominator

• Add 8 to both numerator and denominator

• Multiply numerator and denominator by 8