## anonymous 5 years ago If sin(x) = 1/3 and sec(y) = 5/4 , where x and y lie between 0 and pie/2, evaluate the expression cos(x+y).

1. anonymous

ok you have$sin(x)=\frac{1}{3}$ and you are going to need $cos(x)=\frac{\sqrt{8}}{3}$ by pythatoras

2. anonymous

you also have $sec(y)=\frac{5}{4}$ which means $cos(y)=\frac{4}{5}$

3. anonymous

you also need $sin(y)=\frac{3}{5}$ also by pathagoras

4. anonymous

now $cos(x+y)=cos(x)cos(y)-sin(x)sin(y)$ and now all these numbers are known so you substitute then into the formula

5. anonymous

$\frac{\sqrt{8}}{3}\times \frac{4}{5}-\frac{1}{3}\times \frac{3}{5}$

6. anonymous

=$\frac{8\sqrt{2}-3}{15}$

7. anonymous

could you explain the pythagoras part for me? how is sin x = 1/3 is cos x = sqrt 8 /3. could you please show that work?