How do you find the values of the other five trigonometric functions of the acute angle A with $cos A = \frac{2}{3}$ $cosA=2/3$ ?

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How do you find the values of the other five trigonometric functions of the acute angle A with $cos A = \frac{2}{3}$ $cosA=2/3$ ?

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Answer 1 · 2018-01-12T17:30:58

If $cos A = \frac{2}{3}$ $Cos A = 2/3$
Then, $sec A = \frac{3}{2}$ $Sec A = 3/2$
$sin A$ $Sin A$ = $\sqrt (1 - {(\frac{2}{3})}^{2})$ $√(1-(2/3)^2)$ or $\frac{\sqrt 5}{3}$ $(√5)/3$
Then, $cos e c A = \frac{3}{\sqrt 5}$ $Cosec A = 3/(√5)$
So, $tan A$ $Tan A$ = $\frac{sin A}{cos A}$ $Sin A/Cos A$ or $\frac{2}{\sqrt 5}$ $2/(√5)$
Hence, $cot A$ $Cot A$ = $\frac{\sqrt 5}{2}$ $(√5)/2$

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How do you find the values of the other five trigonometric functions of the acute angle A with $cos A = \frac{2}{3}$ $cosA=2/3$ ?

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