Question

given cosec A =13/5,calculate all other trigonometric ratios ​

Answer 1

$\cosec(a) = \frac{13}{5} \\ \sin(a) = \frac{1}{ \cosec(a) } = \frac{1}{ \frac{13}{5} } = \frac{5}{1 3} \\ { \sin(a) }^{2} + { \cos(a) }^{2} = 1 \\ { { \cos(a) }^{2} } = 1 - { \sin(a) }^{2} = 1 - {( \frac{5}{13}) }^{2} = 1 - ( \frac{25}{169} ) = \frac{169 - 25}{169} = \frac{144}{169} \\ \cos(a) = \frac{12}{13} \\ \tan(a) = \cos(a) + \sin(a) = \frac{12}{13} + \frac{5}{13} = \frac{17}{13} \\ \cot(a) = \frac{1}{ \tan(a) } = \frac{1}{ \frac{17}{13} } = \frac{13}{17} \\ \sec(a) = \frac{1}{ \cos(a) } = \frac{1}{ \frac{12}{13} } = \frac{13}{12}$

Answer 2

Answer:

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