If #tantheta>0# and #csctheta=2#, find all the trigonometrical ratios of #theta#?

1 Answer
Shwetank Mauria · Nityananda
Oct 19, 2017

#sintheta=1/2#, #csctheta=2#, #costheta=sqrt3/2#, #sectheta=2/sqrt3#, #tantheta=1/sqrt3# and #cottheta=sqrt3#

Explanation:

#tantheta > 0# mean #theta# is either in #Q1# or in #Q3#

As #csc theta = 2#, #theta# is in #Q1# only.

As #csctheta=2#, #sin theta = 1/2 = sin 30^@#

Hence #theta = 30 ^@#

So,
#cos 30^@ = sqrt3/2, sec 30^@ = 2/sqrt3, tan 30^@ = 1/sqrt3 = 0.57" which is greater than " 0, cot 30^@ = sqrt3, sin 30^@ = 1/2 and csc 30^@ = 2#

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