What are the values of the other five trigonometric functions of theta, given that cos theta = 5/13, 0<theta<pi/2?

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Answer 1 · 2018-04-24T03:15:25

# cos theta = 5/13#, #sin theta = 12 /13 #, #tan theta = 12/5 #,
#cot theta = 5/12#, #csc theta = 13/12 #, #sec theta = 13/5#

That's a #5,12,13# right triangle, #5^2+12^2=13^2#

#5# is the adjacent or #x# part, #12# is the opposite or #y# part, #13# is the hypotenuse #\sqrt{x^2+y^2}#.

We're in the first quadrant so all the trig functions are positive.

# cos theta = 5/13#

#sin theta = 12 /13 #

#tan theta = 12/5 #

#cot theta = 5/12#

#csc theta = 13/12 #

#sec theta = 13/5#