Using addition of two angles with triangles to evaluate for cosine

The video tutorial explains how to solve a trigonometry problem involving the evaluation of sine and cosine values for angles in different quadrants. The instructor guides through constructing triangles, applying the Pythagorean theorem, and using the cosine of sum formula to find the solution. The process includes detailed calculations and simplification of results, emphasizing the importance of understanding quadrant positions and reducing fractions.

What are the given values for sine of U and cosine of V?

• Sine of U = 3/5, Cosine of V = 7/25

• Sine of U = -7/25, Cosine of V = -3/5

• Sine of U = -3/5, Cosine of V = -7/25

• Sine of U = 7/25, Cosine of V = 3/5

In which quadrant are the angles U and V located?

• Quadrant 4

• Quadrant 2

• Quadrant 1

• Quadrant 3

What theorem is used to find the missing side of the triangle?

• Law of Sines

• Law of Cosines

• Triangle Inequality Theorem

• Pythagorean Theorem

What is the expression used to calculate cosine of U + V?

• sin(U) * cos(V) - cos(U) * sin(V)

• sin(U) * cos(V) + cos(U) * sin(V)

• cos(U) * cos(V) - sin(U) * sin(V)

• cos(U) * cos(V) + sin(U) * sin(V)

What is the cosine of angle U?

• -7/25

• -4/5

• -24/25

• -3/5

What is the final simplified result for cosine of U + V?

• 5/3

• 3/5

• 21/125

• 96/125

Why is it important to reduce the final result?

• To simplify the expression

• To match the unit circle values

• To ensure accuracy

• To make calculations easier