Question

Review the diagram of the unit circle. A unit circle. Point P is on the circle on the x-axis at (1, 0). Point S is in quadrant 4 at (cosine (negative v), sine (negative v)). Point Q is in quadrant 1 above point P at (cosine (u), sine (u)). Point R is above point Q at (cosine (u v), sine (u v)). Based on the diagram, which equation can be simplified to derive the cosine sum identity?

1) cos(u + v) = cos(u)cos(v) - sin(u)sin(v)
2) cos(u + v) = cos(u)cos(v) + sin(u)sin(v)
3) cos(u + v) = cos(u) - cos(v) + sin(u)sin(v)
4) cos(u + v) = cos(u) + cos(v) - sin(u)sin(v)

Answer 1

The equation that can be simplified to derive the cosine sum identity based on the diagram of the unit circle is 1) cos(u + v) = cos(u)cos(v) - sin(u)sin(v). The cosine sum identity is a fundamental trigonometric identity that relates the cosine of the sum of two angles to the cosine and sine of the individual angles.

Step-by-step explanation:

The cosine sum identity is a fundamental trigonometric identity that relates the cosine of the sum of two angles to the cosine and sine of the individual angles. It is derived using the unit circle and the trigonometric definitions of cosine and sine.

To explain the step-by-step process of deriving the cosine sum identity, we can break down the diagram of the unit circle and use the definitions of cosine and sine in each quadrant to determine the coordinates of points P, S, Q, and R. By comparing the coordinates and using the cosine and sine functions, we can simplify the equation to arrive at the correct answer.