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Given sin 0=5/6 find cos 0

Given sin 0=5/6 find cos 0-example-1
User Lee Oades
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Based on the identity `sin^2(theta) + cos^2(theta) = 1`, we can solve for `cos(theta)` as follows:

`(sin(theta))^2 + (cos(theta))^2 = 1`

Substituting `sin(theta) = 5/6`:

`(5/6)^2 + (cos(theta))^2 = 1`

Simplifying:

`25/36 + (cos(theta))^2 = 1`

`(cos(theta))^2 = 1 - 25/36`

`(cos(theta))^2 = 11/36`

Taking the square root of both sides:

`cos(theta) = +/- sqrt(11)/6`

Since we know that `sin(theta) = 5/6`, we can conclude that `cos(theta)` is the positive value `cos(theta) = sqrt(11)/6`.

Therefore, `cos(theta) = sqrt(11)/6`.
User DusteD
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