Assume that #theta# is an acute angle in a right triangle satisfying the given condition. Evaluate the remaining trigonometric functions ? #sin theta= 4/11#

Find
#cos theta=#
#tan theta=#
#csc theta=#
#sec theta=#
#cot theta=#

1 Answer
Daniel L.
May 13, 2018

See explanation.

Explanation:

First we can notice that all the values are positive because the angle is accute (i.e. it is located in #Q1#).

To calculate #costheta# we can use the identity saying that for any angle we have:

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

If we use the given value we get:

#(4/11)^2+cos^2theta=1#

#cos^2theta=1-(4/11)^2#

#cos^2theta=1-16/121=105/121#

#costheta=sqrt(105)/11#

Now having #sintheta# and #costheta# we can calculate the remaining functions:

#tantheta=sintheta/costheta# ##

#tantheta=4/11-:sqrt(105)/11=4/11*11/sqrt(105)=4/sqrt(105)=(4sqrt(105))/105#

#cottheta=1/tantheta=sqrt(105)/4#

#sectheta=1/costheta=11/sqrt(105)=(11sqrt(105))/105#

#csctheta=1/sintheta=11/4=2 3/4#

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