Question

Let sin 0 = 4/9. Find the exact value of cos 0.

Answer 1

we have the following

`\sin \theta=(4)/(9)`

sin of an angle is the same as:

`\sin \theta=(opposite)/(hypotenuse)`

therefore we can create the following right triangle:

we can calculate the adjacent side using the pythagorean theorem

`h^2=a^2+b^2`

where h is the hypotenuse, a is the adjacent side and b the opposite side to the angle.

thus, the adjacent side is:

`a=\sqrt[]{h^2-b^2}=\sqrt[]{9^2-4^2}=\sqrt[]{81-16}=\sqrt[]{65}`

Using that value, we can now calculate cos of the angle

`\cos \theta=(adjacent)/(hypotenuse)`
`\cos \theta=\frac{\sqrt[]{65}}{9}`

which can't be simplify, thus that is the answer for the exact value