How do you sketch a right triangle corresponding to $costheta=5/7$ and find the third side, then find the other five trigonometric functions?

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Answer 1 · 2017-03-10T05:58:37

See below.

$cos theta$ =( adjacent side ) / ( hypotenuse ) $=5/7$

Adjacent side $= 5 k$ ; Hypothenuse $= 7k$

Let opposite side be $x$

By Pythagoras theorem,

$49k^2= 25k^2+x^2$

$49k^2- 25k^2=x^2$

$x^2=24k^2$

$x=sqrt24k$

$x=2sqrt6 k$

Third side = $x=2sqrt6 k$

$sin theta = (2sqrt6) / 7$

$cos theta =5/7$

$tan theta = (2sqrt6) / 5$

$cot theta = 5/(2sqrt6)$

$sec theta =7/5$

$cosec theta =7/ (2sqrt6)$

How do you sketch a right triangle corresponding to costheta=5/7costheta=5/7 and find the third side, then find the other five trigonometric functions?