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) #