Help Solving Trig Homework: Find cos(u+v)

[e^(i Pi)+1=0]

Homework Statement

If Sin(u)=$\frac{\sqrt{2}}{2}$ and cos(v)=$\frac{4}{5}$ and

0≤ u ≤$\frac{∏}{2}$ and $\frac{3∏}{2}$≤ v ≤ 2∏

find cos (u+v)

The Attempt at a Solution

cos(u)=$\frac{\sqrt{2}}{2}$ and cos(v)=$\frac{4}{5}$

Do I just add them together? I feel like I'm missing something, but maybe the problem really is that simple.

 

[SammyS]

Homework Statement

If Sin(u)=$\frac{\sqrt{2}}{2}$ and cos(v)=$\frac{4}{5}$ and

0≤ u ≤$\frac{∏}{2}$ and $\frac{3∏}{2}$≤ v ≤ 2∏

find cos (u+v)

The Attempt at a Solution

cos(u)=$\frac{\sqrt{2}}{2}$ and cos(v)=$\frac{4}{5}$

Do I just add them together? I feel like I'm missing something, but maybe the problem really is that simple.

Use the angle addition identity for cosine .

 

[e^(i Pi)+1=0]

So it would be..

($\frac{\sqrt{2}}{2}$)($\frac{4}{5}$)-($\frac{\sqrt{2}}{2}$)($\frac{-3}{5}$) = $\frac{7\sqrt{2}}{10}$

 

[ehild]

Excellent!

ehild