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I know that $\cot\theta = 4/3$ how do I find $\csc\theta$?

I tried to do $\csc^2\theta - \cot^2\theta = 1$

This gives me $\csc^2\theta = 1 + \cot^2\theta$

this gives $csc^2\theta = 9/9 + 16/9 = 27/9 = \sqrt{3}$

is this wrong? My book gives the answer as $5/3$

I can never go more than $2$ homework problems without getting stuck.

  • 3
    You did everthing right, but 9+16 = 25 not 272011-06-28

3 Answers 3

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Do you know "Soh-Cah-Toa"? That is sine is the opposite side over hypoteneuse, cosine adjacent over hypoteneuse, and tangent is opposite over adjacent. Then cotangent will be adjacent over hypoteneuse. Therefore you have a right triangle where the side adjacent to your angle is 4 and the side across from your angle is 3. Pythagorean Theorem says the hypoteneuse is 5. Therefore cosecant, which is hypoteneuse over opposite is 5/3.

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    @Adam trig functions represent relations between the sides of a right triangle. Excepting some corner cases (like $\theta = \frac{\pi}{2}$) you can always construct a right triangle that "represents" the trig relation.2011-06-28
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If $\cot{(x)} = 4/3$, then we have this picture

<

                 /|                 / |  3            5   /  |               /   |              x-----                4 

Now compute.

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    It would help a bit more simply by being clear about which angle is $\theta$, so as not to confuse Adam...I just added the angle "x" to illustrate your relation.2019-03-20
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I don't see what is your problem here... You know that $csc^2 x= 1+\cot^2 x=1+\frac{16}{9}=\frac{25}{9}$. From here, you get $\csc x=\frac{5}{3}$. It's pure algebra. Just look at what you have and where do you want to get, and as I said, do not rush with computations, since I notice you make very many elementary mistakes.

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    @Adam as I pointed out in my comment, even though you checked 12 times you missed the clear arithmetic error2011-06-28