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Find the cotangentIf sin x = 3/4 and x is in the set (90,180), what is cot x?
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In the 2nd quadrant, the values of cotangent function are negative.
To determine the value of cotangent function, in the given conditions, we'll apply Pythagorean identity:
1 + (cot x)^2 = 1/(sin x)^2
(cot x)^2 = 1/(sin x)^2 - 1
cot x = - sqrt [1/(sin x)^2 - 1]
cot x = - sqrt (16/9 - 1)
cot x = - (sqrt 7)/3
We'll keep only the negative value for cotangent function
Posted by giorgiana1976 on May 25, 2011 at 1:16 AM (Answer #2)
You need to use the following trigonometric identity, such that:
`cot x = cos x/sin x`
The problem provides `sin x = 3/4` , hence, using the fundamental formula of trigonometry, you may find `cos x` , such that:
`cos x = +-sqrt(1 - sin^2 x)`
`cos x = +- sqrt(1 - 9/16) => cos x = +-sqrt(7/16)`
You should remember that for any angle `x in (90^o, 180^o)` , the cosine is negative and sine is positive, hence cotangent is negative, such that:
`cos x = -sqrt7/4`
`cot x = -(sqrt7/4)/(3/4) => cot x = -sqrt7/3`
Hence, evaluating cot x, under the given conditions, yields `cot x = -sqrt7/3.`
Posted by sciencesolve on March 5, 2013 at 5:44 PM (Answer #3)
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