Trigonometric Functions and Quadrants

The video tutorial explains how to find the exact values of trigonometric functions using half-angle identities. It starts with a given tangent value in quadrant four and proceeds to find the cosine, sine, and tangent of half the angle. The tutorial uses reference angles, triangles, and the Pythagorean theorem to derive these values, emphasizing the importance of quadrant-specific signs for trigonometric functions.

What is the value of tangent u in quadrant four?

• -7/8

• 7/8

• -8/7

• 8/7

In which quadrant is angle u located?

• Quadrant II

• Quadrant I

• Quadrant IV

• Quadrant III

What is the hypotenuse of the reference triangle for angle u?

• Square root of 81

• Square root of 64

• Square root of 49

• Square root of 113

What is the cosine of angle u?

• 7 divided by the square root of 113

• 8 divided by the square root of 113

• -7 divided by the square root of 113

• -8 divided by the square root of 113

In which quadrant does u/2 terminate?

• Quadrant I

• Quadrant IV

• Quadrant II

• Quadrant III

What is the sign of sine of u/2?

• Positive

• Negative

• Zero

• Undefined

What is the exact value of sine of u/2?

• Square root of (1/2 - 7/(2*sqrt(113)))

• Square root of (1/2 + 7/(2*sqrt(113)))

• -Square root of (1/2 + 7/(2*sqrt(113)))

• -Square root of (1/2 - 7/(2*sqrt(113)))

What is the sign of cosine of u/2?

• Undefined

• Zero

• Positive

• Negative

What is the exact value of cosine of u/2?

• Square root of (1/2 + 7/(2*sqrt(113)))

• -Square root of (1/2 + 7/(2*sqrt(113)))

• Square root of (1/2 - 7/(2*sqrt(113)))

• -Square root of (1/2 - 7/(2*sqrt(113)))

What is the exact value of tangent of u/2?

• 8/(sqrt(113) - 7)

• -8/(sqrt(113) - 7)

• 8/(sqrt(113) + 7)

• -8/(sqrt(113) + 7)