Originally Posted by

**Archie Meade** ok,

just use $\displaystyle cos\alpha=\frac{4}{5}=\frac{adjacent}{hypotenuse}$

Adjacent=4, hypotenuse=5.

Draw the triangle.

Pythagoras' theorem gives $\displaystyle (opposite)^2+(adjacent)^2=(hypotenuse)^2$

Use this to find the length of the 3rd side.

Then write $\displaystyle sin\alpha$

Finally use the trigonometric identity.

You need $\displaystyle sin\beta$ and $\displaystyle cos\beta$ also.

You get these when you have the 3rd side of the 2nd triangle.

$\displaystyle tan\beta$ gives you 2 of the 3 sides of that one.

Pythagoras theorem gets you the 3rd.

Then you can write $\displaystyle cos\beta$ and $\displaystyle sin\beta$

before using the trigonometric identity.