Given two triangles determine the difference of the two angles using cosine

The video tutorial explains how to handle trigonometric functions when values are not on the unit circle. It emphasizes the importance of creating triangles in Quadrant 2 and using the Pythagorean theorem to find missing sides. The tutorial also covers calculating the cosine of U - V using specific formulas, ensuring students understand the process of applying trigonometric identities and theorems.

Why is it necessary to create a triangle when evaluating trigonometric functions not on the unit circle?

• To find the exact coordinates on the unit circle

• To apply the Pythagorean theorem

• To simplify the calculation of trigonometric functions

• To determine the quadrant of the angle

What is the correct way to draw a triangle in a specific quadrant?

• Draw it randomly

• Ensure it is perpendicular to the X-axis

• Align it with the hypotenuse

• Make it parallel to the Y-axis

What is a Pythagorean triple?

• A set of three trigonometric identities

• A set of three points on the unit circle

• A set of three integers that satisfy the Pythagorean theorem

• A set of three angles that sum up to 180 degrees

How can you find the missing side of a right triangle using the Pythagorean theorem?

• By multiplying the two known sides

• By subtracting the square of one side from the square of the hypotenuse

• By dividing the hypotenuse by one of the sides

• By adding the squares of the two known sides

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

• cos(U - V) = sin(U) * sin(V) + cos(U) * cos(V)

• cos(U - V) = cos(U) * cos(V) - sin(U) * sin(V)

• cos(U - V) = cos(U) * sin(V) + sin(U) * cos(V)

• cos(U - V) = sin(U) * cos(V) - cos(U) * sin(V)

What values are used to calculate the cosine of U - V in this example?

• cos(U) = 5/13, cos(V) = -3/5, sin(U) = 5/13, sin(V) = 4/5

• cos(U) = -3/5, cos(V) = 5/13, sin(U) = 5/13, sin(V) = 4/5

• cos(U) = 5/13, cos(V) = -3/5, sin(U) = 4/5, sin(V) = 5/13

• cos(U) = -3/5, cos(V) = 5/13, sin(U) = 4/5, sin(V) = 5/13

What is the final result for the cosine of U - V in this problem?

• 36/65

• 65/56

• 65/36

• 56/65