The discussion revolves around finding cos(u+v) given specific values for sin(u) and cos(v), along with defined ranges for the angles u and v. The problem is situated within the context of trigonometric identities and angle addition formulas.
There is a mix of attempts to apply the angle addition identity, with one participant providing a calculation based on the identity. However, the discussion does not reach a consensus, as another participant expresses uncertainty about the simplicity of the problem.
Participants are working under the constraints of the given ranges for u and v, which may influence the signs of the trigonometric functions involved.
Use the angle addition identity for cosine .e^(i Pi)+1=0 said:Homework Statement
If Sin(u)=[itex]\frac{\sqrt{2}}{2}[/itex] and cos(v)=[itex]\frac{4}{5}[/itex] and
0≤ u ≤[itex]\frac{∏}{2}[/itex] and [itex]\frac{3∏}{2}[/itex]≤ v ≤ 2∏
find cos (u+v)
The Attempt at a Solution
cos(u)=[itex]\frac{\sqrt{2}}{2}[/itex] and cos(v)=[itex]\frac{4}{5}[/itex]
Do I just add them together? I feel like I'm missing something, but maybe the problem really is that simple.