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Fiesta28 [93]
2 years ago
14

If cot theta = 2/3, what is the value of csc theta?

Mathematics
2 answers:
galben [10]2 years ago
7 0
Hi,\dfrac{2}{3} =cotg\ \theta =\dfrac{cos\ \theta}{sin\ \theta}\\\\
\Rightarrow\ 2*sin\ \theta=3*cos\ \theta\\\\
\Rightarrow\ 2*sin\ \theta=3* \sqrt{1-sin^2\ \theta} \\\\
\Rightarrow\ 4*sin^2\ \theta=9* (1-sin^2\ \theta}) \\\\
\Rightarrow\ 13*sin^2\ \theta=9) \\\\
\Rightarrow\ sin\ \theta= \dfrac{3}{ \sqrt{13} } \\\\

\Rightarrow\  \dfrac{1}{sin\ \theta}=cosec\ \theta= \dfrac{ \sqrt{13} }{3} \\\\

\boxed{cosec\ \theta= \dfrac{ \sqrt{13} }{3} }

Maybe "cosec a, cotg a" (in  french) is written "csc a,cot a" in american

Charra [1.4K]2 years ago
6 0
Sqrt 13/3

There is a great explanation at https://socratic.org/questions/if-cot-theta-2-3-what-is-the-value-of-csc-theta
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