Find the function values of cos θ, tan θ, sec θ, csc θ and cot θ ?

If sin θ = −(4)/(5)
and cos θ < 0, in which quadrant is θ? Find the function values of
cos θ, tan θ, sec θ, csc θ and cot θ.

1 Answer
Sahar Mulla ❤
Feb 13, 2018

Given that, #sin θ = (−4)/(5)#

applying the identity, #sin^2theta + cos^2 theta = 1#

#cos^2 theta = 1-sin^2theta #

#cos^2 theta = 1- ((-4)/5)^2 #

#cos^2 theta = 1- 16/25 = 9/25 #

#costheta = sqrt(9/25) = +-3/5 #

its given that, #cos θ < 0# ; #color(magenta)(costheta =(-3)/5 #
Since, both #sintheta# and #costheta# are negative, #theta# lies in the #color(red)("third quadrant")#.

#tantheta = sintheta/costheta#
#=(-4)/5 xx 5/(-3) => color(magenta)(tantheta= 4/3#

#sec θ = 1/costheta => color(magenta)(sec theta=(-5)/3#

#csc θ = 1/sintheta => color(magenta)(csctheta = (-5)/4#

#cottheta = costheta/sintheta = 1/tantheta => color(magenta)(cottheta=3/4#

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