Trigonometric Functions and Identities

The video tutorial explains how to find the exact values of sine, cosine, and tangent for an angle u divided by two, given that cosine of u is negative 11/15 in quadrant three. Using half-angle identities, the tutorial demonstrates the calculations step-by-step, considering the signs of trigonometric functions based on the quadrant in which the angle terminates. The tutorial provides a clear explanation of the process, including simplification techniques and the rationale behind each step.

In which quadrant does angle u terminate if cosine of u is negative?

• Quadrant I

• Quadrant III

• Quadrant IV

• Quadrant II

What is the sign of sine of u/2 if angle u/2 is in quadrant II?

• Undefined

• Zero

• Negative

• Positive

How do you simplify the expression 1 - (-11/15) when calculating sine of u/2?

• 1 + 15/11

• 1 - 15/11

• 1 + 11/15

• 1 - 11/15

What is the exact value of sine of u/2 in terms of square roots?

• Square root of 13/15

• Square root of 15/13

• Square root of 26/15

• Square root of 15/26

What is the sign of cosine of u/2 if angle u/2 is in quadrant II?

• Undefined

• Zero

• Negative

• Positive

How do you simplify the expression 1 + (-11/15) when calculating cosine of u/2?

• 1 - 11/15

• 1 + 11/15

• 1 + 15/11

• 1 - 15/11

What is the exact value of cosine of u/2 in terms of square roots?

• Square root of 2/15

• Negative square root of 15/2

• Square root of 15/2

• Negative square root of 2/15

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

• Cosine of u divided by sine of u

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

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

• Sine of u divided by cosine of u

What is the exact value of tangent of u/2 in terms of square roots?

• Square root of 13/2

• Negative square root of 2/13

• Square root of 2/13

• Negative square root of 13/2

What is the final step in finding the exact value of tangent of u/2?

• Add sine and cosine

• Multiply sine and cosine values

• Subtract cosine from sine

• Divide sine by cosine