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

Let sin 0 = 4/9. Find the exact value of cos 0.-example-1

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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

Let sin 0 = 4/9. Find the exact value of cos 0.-example-1
User Keryn Knight
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