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