Evaluating the difference of two angles for the cosine function

The video tutorial covers the evaluation of the cosine of the difference of two angles, focusing on creating triangles in the second quadrant and applying the Pythagorean theorem. The instructor explains the importance of using the correct signs for triangle sides based on their quadrant and demonstrates the application of the cosine difference formula. The session concludes with a Q&A segment addressing common student mistakes.

What is the main challenge when the angles do not intersect the unit circle?

• Finding the exact coordinates on the circle

• Using the sine and cosine definitions

• Applying the Pythagorean theorem

• Creating a triangle in the correct quadrant

Why must the triangle be perpendicular to the X-axis?

• To ensure it is a right triangle

• To avoid using the Pythagorean theorem

• To simplify the sine calculation

• To align with the Y-axis

In the second quadrant, what is the sign of the adjacent side?

• Zero

• Negative

• Positive

• Undefined

What is the formula for the cosine of the difference of two angles?

• cos(U) * cos(V) - sin(U) * sin(V)

• cos(U) * cos(V) + sin(U) * sin(V)

• sin(U) * cos(V) - cos(U) * sin(V)

• sin(U) * cos(V) + cos(U) * sin(V)

What is the final result of the cosine difference calculation?

• 36/65

• 20/65

• 65/65

• 56/65